What does Galatians 4:31 mean?

Paul concludes his allegory comparing those who insist on living under the law, even after Christ has come, and those who trust in Christ alone to justify them before God. The law-followers are like Ishmael, Abraham's son by a slave woman (Genesis 16:1–3), born as a result of human scheming and human efforts. They remain in slavery to their own sin, and they will not receive any part of the inheritance of God's promises to Abraham.

Christians, those who have abandoned hope in the law to save them, trusting in Christ alone, are like Isaac. He was the son of the free woman born as a result of the promise of God (Genesis 21:1–3). He was not born as the result of human effort or good works. Christians, also, are born into God's family by the work of the Holy Spirit, and absolutely no work of their own. They are free. As Paul writes in this verse, we—all who are saved, born-again Christians—are symbolically the children of the free woman.