What does Galatians 4:24 mean?
Paul is aware that the false teachers are arguing from the Old Testament Scriptures that the Galatian Christians must follow the law in order to be saved (Galatians 2:4). He has asked if they have really listened to the law (Galatians 4:21). To help them see why faith in Christ is superior, Paul is building an illustration about Christ and the law from the two sons of Abraham, Isaac and Ishmael.He has described Ishmael, born of a slave-girl (Genesis 16:1–2), as being born according the flesh. Isaac, however, was the child of God's promise, born of the free woman Sarah, Abraham's wife (Genesis 21:1–3). Now Paul lays out the careful allegory he is creating. Hagar, the slave-woman, represents one covenant, while Sarah, the free woman, represents another.
Specifically, Hagar represents the covenant from Mount Sinai. Mount Sinai is where God gave His law for Israel to Moses, described beginning in Exodus chapter 19. In this letter to the Galatians, Paul has already shown that to live under the law of Moses is to live in slavery to our own sin. The law reveals our sin, but it does not offer a way to be free from it (Galatians 3:19–25).
Hagar, then, as the slave woman, represents the covenant of the law between God and His people, Israel. All born under this covenant are born into slavery, just as Ishmael, Hagar's son with Abraham, was born into slavery. Importantly, we should note that this is not God's ultimate plan—there is a "better way" planned for us.