Nearly all Christian faiths believe that the term "children of God" refers to those who have accepted Christ and have been adopted by Him through being born again into His household, and this is certainly true in the context of salvation. The Church of Jesus Christ of Latter-day Saints also believes this as well in the specific way that Paul speaks of it.
However, through revelation, we have come to understand that all of mankind are also children of God in a real and literal sense. In other words, the term "children of God" has a double meaning. It can refer to those who have made the conscious decision to become followers of Christ, taking upon themselves His name, and pledging to keep His commandments. In this sense a child of God is one who has been reborn by God's Holy Spirit and are no longer a follower of the ways of the world but now have a desire to be lead of the Spirit. But there is another sense in which we are children of God.
Long before Christ offered Himself up as a sacrifice on the cross to atone for our sins, He taught His disciples to pray saying, "Our Father which art in heaven…" All Christians believe that Jesus is the real and literal Son of God, which is why He can truly call God His Father, but He taught us to address God as our Father as well. In fact, when Jesus was first resurrected and Mary went to touch Him He told her, "go to my brethren, and say unto them, I ascend unto my Father, and your Father; and to my God, and your God." (John 20:17, emphasis added).
God is not only the Father of Jesus, in a very real and literal way, but that same God is also our Father as well in the same way. Most Christians believe that man is made up of both a physical body and a spirit, and that it is the spirit of man that gives him life. We know that the physical body comes from the uniting of a man's sperm with a woman's egg, but where does a person's spirit come from?
Modern revelation teaches that we were born as spirit beings to our Father in heaven, meaning that God begat us first in heaven. However, instead of having a physical body as we now do, we existed back then as spirit beings. Nevertheless, we were still His children and He was our Father, and our relationship to Him is the same as what earthly children have to their earthly parents. That is why we call God "our Father" who lives in heaven.
Because of this relationship, the LDS Church teaches that we are all children of God, but this phrase has been used so often that its true significance is often trivialized. For many LDS members, the phrase "I am a child of God" simply means that God is our true Father and that we hope to someday return back to Him. However, this phrase has a much greater meaning to it than that.
When we lived in heaven as spirit beings, we didn't refer to our heavenly Father as God because, to us, He was simply "Father." For example, imagine a child being born to the President of the United States. As they grow up living in the White House, they don't address their father as "president," as does everyone else because to them, that's not who he is. To them he is their father who just happens to be a very busy and powerful man.
And the same is true of all fathers. Whether a man is the president of a company, or a successful salesman, or is just an assembly-line factory worker, a child identifies his male parent as "father," even though they may know what their father does for a living. And so it was with us when we lived in heaven. We knew we lived in heaven and we knew that our Father was a very busy, important, and powerful person, but to us He was not "God," (although we knew that was His title). To us He was simply "Father."
However, our Father is no ordinary Being. Despite the fact that He is our Father, He is also God, who wields tremendous power and authority. That means we are not ordinary children. We are the sons and daughters of a God and, as such, we are special beings.
To illustrate this point, during its long history, England was at one time the superpower of the world and no other nation could withstand its awesome naval and military might. During this time, England was ruled over by a king, which made him the most powerful man in the world.
Children born to this king grew up in his household and enjoyed all the amenities and privileges that the royal house offered to its king. Yet, even though these children knew their father was the king and was a very important person (even though they may not have fully understood all of his responsibilities and duties), they nonetheless still referred to him as "father."
And the same was true in reverse. The king referred to his offspring as children, or sons or daughters, but to everyone else they were a prince or a princess and were addressed and treated that way. Because of this, they were given the best clothing to wear, ate the best food, received the best instruction, and had numerous servants attending to their every need.
Yet, while they were young, living in the royal household, these children of the king saw nothing unusual about their living conditions because they knew no other lifestyle. To them, it was just as natural as breathing that they had all of these privileges.
And it was the same with us growing up in heaven. When we say that we are children of God, we can think of that as if saying, we are the offspring of the King of England, or the children of the Pharaoh, or the son or daughter of the Emperor of Rome. We are royalty! Each male person on earth is a prince of God and each female person on earth is a princess of God!
Yet, when we lose sight of that fact is when we are inclined to act like common street urchins, engaging in dishonest practices, theft, drunkenness, debauchery, and other forms of behavior that are unbecoming of a child of royalty and which sullies the name and reputation of their glorious parents.
Although it is true that many earthly kings have engaged in corrupt behavior themselves, that is not true of the King of heaven. God is totally righteous and never engages in doing anything unrighteous, therefore, when His children behave in unrighteous ways, it does bring dishonor upon their heavenly Father.
However, children of royalty are not only privileged but they also have great responsibilities that no ordinary child will ever have. An earthly king will someday die, therefore one of his children will someday take over the reigns of government. For this reason, children of royalty are tutored and prepared to inherit the throne of their father.
They are taught to speak fluently in several different languages so they can conduct business with foreign nations. They are taught to read and write so they can then be taught law, philosophy, mathematics, finances, and a host of other subjects necessary to understand in order to wisely rule over their father's kingdom.
Boys especially are taught the art of warfare. They are rigorously trained to learn how to fight, how to command men, and the strategies for winning battles because, as a king, they will have control over their country's entire military land and naval forces, and therefore must know how to effectively use them to defend their nation.
At an early age these princes go into battle with seasoned warriors. Then, as they learn their lessons well, they are put in command of a small regiment, then a larger company, and then perhaps an entire division, all for the purpose of teaching them the skills they will need when they someday become the king.
But even before their father dies, a prince (or duke, which is another royal title) may be given a large tract of land to rule over, which gives them the training on how to be a good governor. We see this in such titles as the Prince of Wales or the Duke of Edinburgh. Sometimes a son will be made an ambassador to represent their father, the king, with other heads of state.
All of this training is designed to help the children of the king to someday govern a kingdom and fulfill the duties and responsibilities that their father now is able to do. And this same situation applies to us as the children of God. We are being trained to someday do what our Father in heaven now does. A major part of why we are here on this earth is to be taught and learn all the principles we will need to know and live by in order for us to someday rule and reign with Christ forever (Revelation 5:10).
But when we forget who we are, and lose sight of our royal heritage, and what we can become, we are like college kids who take their precious learning time and waste it on partying and having riotous fun instead of studying and preparing themselves for their future careers.
But there is another very important aspect of being a child of God.
Both morally and legally, children are required to obey their parents and that's because parents have a great responsibility when it comes to raising them. Nearly all civilized societies, and many that are not civilized, follow this rule because it is well understood that children need guidance from adults who not only know and understand more than their children but who love and have their best interests at heart.
As such, parents set rules of behavior in their homes that are meant to teach their children the values of life that will help them to become successful adults themselves. These rules include such things as helping their children to learn proper behavior, developing skills, improving talents, getting along in society, gaining a positive attitude, and other traits they will need to flourish and be happy as they go forth into the world as adults.
Yet, in their immaturity, especially among teenagers, children have a tendency to think that they don't need to follow the rules their parents have set down and they often rebel at following their parent's decrees. When that happens, parents employ a number of methods that are designed to teach their children the error of their thinking and behavior. Some of those methods may be mild and gentle in their application while others may be firm and strong. But whatever method a parent uses, it is always meant to help their child to become a better person.
Our Father, who lives in heaven, is no different a parent and many times we, His children, are no different than teenagers who think that we don't have to follow the rules that Father has given us. But, if we truly are children of God then we have a sacred duty to be obedient to our heavenly Father, regardless if He is a God or not. And since He is a God, who is so powerful that even the universe obeys His commands, how much more should we, His divine offspring, show Him the respect He rightly deserves, by obeying His commands, especially after all He blesses us with?
As much as we may sometimes not like the rules God gives us, they are all based on eternal laws, which are not only the very laws that God Himself follows but are the laws by which He is able to maintain His power and authority.
If we are children of God then we are entitled to participate in the family inheritance, which means we can receive all the glory, majesty, power, dominion, and authority that our Father now has. But to obtain these things we have to be willing to abide by the same eternal laws that He does. Those who are not willing to do that will forfeit their inheritance.
All the commandments that God gives us are meant not only to teach us what those eternal laws are but, more importantly, how to properly live them until they become second nature to us. The more we procrastinate keeping God's commandments or the less we keep them with all of our heart, mind, and soul, the more we procrastinate receiving our inheritance.
To truly know and understand that we are literal sons and daughters of God means that we know and understand what our eternal destiny can be and strive to work diligently to obtain what can rightfully be ours. But it is when we lose sight of who we truly are and what we can become that we fall prey to following the philosophies, habits, and customs of a world that believes in living a life that is contrary to nearly every eternal principle.
Truth is eternal and so is love. Truth is being honest, trustworthy, honorable, and having integrity. Truth embodies dealing righteously and with true justice in all of our interactions with others. Love is the showing forth of kindness, patience, mercy, and deeply caring for the needs of others. On the other hand, the world teaches us to lie, steal, cheat, and to deal deceitfully with others in order to take advantage of them. The world encourages us to hate, be jealous, be selfish, and to be quick to find fault with others, criticizing them, especially with the intent to do them harm.
We refer to these unrighteous tendencies as "weaknesses of the flesh" but when we have a full realization of who we are, it becomes easier for us to reject the ways of the world and to live according to the ways of God. Yet the world does all in its power to blind us to this realization so it can rob us of our heavenly reward.
But our Father in heaven has not left us alone to overcome these tendencies by ourselves. As children of God, our Father has a parent's love for each of us and wants us to grow to our full potential, therefore He watches over each and every one of His children with a love that only a parent can have. He is interested in our success and, in fact, is doing all He can to help us to be fully prepared to someday obtain our full inheritance.
When we realize our true relationship to God, our Father in heaven, and how much He loves and cares for us, we are saved from becoming discouraged knowing that no matter what we do or how many times we fail, or how many weaknesses we may have, our heavenly Father not only still loves us but is always there to help us to grow to become more like Him, even if that means applying some form of discipline now and then. It is when we forget our relationship to God that we begin to imagine that He could never love us or forgive us. No righteous parent would ever do that to their children, and God is the most righteous parent there is.
This is what it means when we say "I am a child of God."