What does John 8:17 mean?

It is interesting that Jesus uses the phrase "your Law" here. Most likely, He is referring to Deuteronomy 17:6 or Deuteronomy 19:15. Generally, when Jesus refers to the Old Testament, He calls it "the Law" or "the law of Moses" or "the Scriptures." The words used here might mean that Jesus is speaking of some other, non-scriptural rabbinic law. Then again, it might also show how personal this debate is. In this conversation, the Pharisees will question Jesus' birth (John 8:41) and His sanity (John 8:48), and they will even try to kill Him (John 8:59). Jesus has already criticized the judgment of these opposing religious leaders (John 8:15). Later, He will claim that they do not know God (John 8:19), that they are children of the Devil (John 8:44), and that they are liars (John 8:55).

The Pharisees specifically challenged Jesus' claim to be "the light of the world" (John 8:12). This is a grand suggestion, implying that Jesus is the sole source of both salvation and spiritual wisdom. Earlier in His ministry, Jesus agreed that some claims should be supported with earthly evidence; He provided that to prove His claims (John 5:30–47). Now, however, Jesus is speaking of heavenly issues, which no other person has seen or experienced. To testify about Himself is perfectly legitimate. Even more so, Jesus has the testimony of a second person: God the Father (John 8:18).