What does Romans 10:4 mean?

Paul has shown throughout Romans that the law cannot save anyone. Nobody can keep the law. He wrote in Romans 3:23 that all have sinned and fall short of God's glory, even those who try to follow the law.

Now Paul shows that the law was not meant to stand on its own forever. It always pointed forward to Jesus Christ. As Paul puts it, Christ was always intended to be "the end of the law." He kept it perfectly and fulfilled its righteous requirements once and for all.

Now Christ's righteousness is available to everyone who believes in Him. This is an idea explored in greater detail in the book of Hebrews. There, the writer—possibly Paul himself—explains exactly how God had always intended to bring a new covenant. That covenant was established by Christ, and in Christ, and was meant to end man's dependence on rituals and animal sacrifices (Hebrews 8).