What does Galatians 3:10 mean?

For the false teachers known as the Judaizers, the truth seemed obvious. They were convinced nobody could be included in God's family unless he was circumcised and followed the law of Moses (Galatians 2:4). That, for them, was the clear teaching of the Old Testament. Paul has showed from the Old Testament Scriptures that, in fact, Abraham himself was counted as righteous before God—"justified"—when he believed the Lord (Galatians 3:6). Now Paul begins to show that the rules and rituals given in the Law cannot save anyone. They can only condemn those who try to follow them.

Again, Paul quotes Moses, this time from Deuteronomy 27:26. God says to the Israelites that everyone who does not "do" everything written in the Book of the Law will be cursed. In other words, everyone who tries to follow the law in order to be saved is always under the threat of being cursed by God. As Paul will go on to show, nobody is able to do everything the law says to do perfectly. Life under law, therefore, is life under God's curse.

Paul will continue exploring this idea, showing that salvation can be found only through faith and not through the law.