What does Galatians 3:13 mean?

Paul spent the previous verses arguing from the Old Testament Scriptures themselves that the law cannot save us. The Judaizers are trying to convince the Christians in Galatia that they need to believe in Jesus, and in addition they need to continue to follow the law of Moses (Galatians 2:4). From Deuteronomy, Habakkuk, and Leviticus, Paul has shown that to live by faith and to live under the law are not compatible. They can't be merged.

So what are we to do? Paul showed that living under the law is to spend our days under the threat of being cursed by God for breaking the law. Unfortunately, we all break it somehow, meaning that according to the law all men are doomed. We're cursed. Now Paul turns to the answer and the focus of all of his teaching: Jesus Christ.

Christ did for us what we could not do. He redeemed us from the curse of the law. The word "redeemed," from the Greek exēgorasen, specifically refers to buying someone out of slavery. Christ did that for us, Paul says, by taking our curse on Himself. Paul again quotes from Deuteronomy: Everyone hanged on a tree is cursed (Deuteronomy 21:23). Even the way Jesus was killed was evidence that He had become cursed in our place.

This great verse contains the essence of the "good news"—the "gospel"—of Jesus in a nutshell. Because none of us could follow the law without breaking it, all of us were cursed by it. We were separated from God, not declared righteous by Him. Then Christ stepped in and took our curse on Himself and paid the price of the curse, which is death and separation from God. That frees us from the law and creates the opportunity for us to be saved by faith.