If the first thing you thought of when you read the title above was the song Born Free, you have definitely dated yourself! "Born free / as free as the wind blows / as free as the grass grows / born free, to follow your heart..." But the Bible was talking about being born free a long time before that song came along!
Paul wants to illustrate to you the difference between being born a slave, and being born free. He uses an illustration from Abraham's life: Sarah vs. Hagar. Sarah was Abraham's wife, and Hagar was Abraham's servant (and, later, concubine). You find their story in Genesis --- which, ironically, is the first of the Five Books of the Law that the Jewish cultists were so fond of praising.
Abraham has two sons. One was Ishmael, born of the slave woman Hagar. There was nothing miraculous about Ishmael's birth. Abraham was still potent, and Hagar could still bear children. The other son was named Isaac, born of the free woman Sarah. His birth was miraculous. Abraham was a dried-up old man, and Sarah was well past menopause. Isaac's birth was the product of the miraculous power of the Holy Spirit, working through God's promise.
Paul says the two women illustrate two covenants. Paul isn't denying their historical realness, but he uses them to make a point. Hagar represents the law-covenant God gave the Jews at Mount Sinai, and that then sums up Jerusalem and its people. The Sinai covenant was a covenant of slavery.
But, Paul says, there is another Jerusalem. Not the one located on Mount Zion, the earthly one we know today. No, there is a heavenly Jerusalem, the heavenly city of God. Paul says that believers are citizens ("children") of that Jerusalem. That is our "motherland." Not only that, but we are Isaac's brothers. How so? Because we too are born of a promise. The promise to save, by miraculous power, all who call on the name of the Lord Jesus Christ!
The Jews were persecuting the Christians at the time Paul wrote Galatians, and in that way they were acting like their spiritual ancestor Ishmael. Just as the children of Ishmael persecuted the children of Isaac, the Jews persecuted followers of Christ. The Jews weren't descended from Ishmael physically, but they were his children in a spiritual sense.
Paul then gives a command: Cast out the slave woman and her son! For the son of the slave woman shall not inherit alongside the son of promise. Cast out of the church all those who preach salvation by law! For none of them shall be permitted into the kingdom of God when Christ comes for His people!
God's will is that there be a zero-tolerance rule in our churches for anyone who teaches that we must keep commandments to be saved. It is one thing to counsel confused Christians, as Paul is doing in this letter. It is quite another thing to know the Gospel of free grace, and then knowingly reject it and pollute it.
We Christians are not "of" the Sinai covenant, in any way, shape, or form. We are "of" the Abrahamic covenant -- specifically, the bit about God blessing the nations. God has reversed the curse in Christ! We have received the blessing of new life and everlasting hope! We are not subject to Moses' Law.