Galatians 4:1-7 (ESV)
I mean that the heir, as long as he is a child, is no different from a slave, though he is the owner of everything,  but he is under guardians and managers until the date set by his father.  In the same way we also, when we were children, were enslaved to the elementary principles of the world.  But when the fullness of time had come, God sent forth his Son, born of woman, born under the law,  to redeem those who were under the law, so that we might receive adoption as sons.  And because you are sons, God has sent the Spirit of his Son into our hearts, crying, "Abba! Father!"  So you are no longer a slave, but a son, and if a son, then an heir through God.
For an aside I want to note a rather serious translation change I have noticed in the Gospel of John. John 1:14 used to read only begotten Son of the Father, in more recent translations (specifically the ESV) it reads only Son from the Father. I suppose that the translators may have figured that from conveys the begottenness of Jesus Christ, and so they didn’t actually have to translate begotten. At least they didn’t leave it “only Son of the Father.” I still think that “monogeneis” should be translated “only begotten,” I don’t care what you do with the preposition “para.” Prepositions are sloppy in every language. So “only Son from the Father” leaves out quite a bit, and allows for confusion on a massive scale. If Jesus is the only Son then I am not a son. This is the connection to today’s reading. Paul says we are sons. (I think you women can feel free to read in daughter here.) Of course if Jesus is not begotten of the Father, then He isn’t God, He would not be of the same substance as the Father. A rabbit is begotten of a rabbit, and therefore shares the same substance as the rabbit, who begat it. A rabbit cannot be begotten of a turtle. (Unless the evolutionary theories are correct.) If He isn’t God then His sacrifice on the cross really didn’t accomplish much for us, least of all redemption from the law that we might be adopted as Sons. A lot hangs on this word begotten.
The point is we are children of God who stand to inherit from him. We are heirs, not slaves. Children are heirs. We stand to inherit. Children don’t do anything to receive their inheritance. The inheritance is theirs by virtue of them being children. Of course in the good old days it was only the son who inherited, though the daughter got a dowry. This I believe is the reason Paul uses the term son and not daughter through most of this section. Thought at the beginning he uses the term child, which is somewhat more gender neutral and may be allowed to color this whole discourse.
We poor sinners have been adopted into a rich family, we stand to inherit eternal life, a mansion, and all the glory one could imagine. We are children of God. He is our Father now. We have a lot to be happy about.