What does John 8:4 mean?

The use of "Teacher" here is probably sarcastic. In Greek, the term Didaskale does not carry an automatic sense of respect, as does the word Rhabbi (John 3:2). Jesus is speaking to the crowd, and the Pharisees are looking for a way to discredit Him with His followers. As they bring a guilty woman into the area and place her in the middle of the crowd (John 8:3), they highlight Jesus' reputation by referring to Him as "Teacher." This is key to their scheme: to prove to the people that Jesus is not a figure worth following.

It is unlikely the woman was caught "in the act" mere moments prior and dragged directly in front of Jesus. More than likely, she'd been previously found out and carefully chosen by the Pharisees in advance. Oddly, this intense preparation left out something crucial.

The Pharisees will point to Old Testament law, which required the death penalty for adulterers (Leviticus 20:10; Deuteronomy 22:22). They will fail to mention that the Law did not require that they stone such women. It said they should stone both guilty persons. If this woman was caught in the middle of an act of adultery, that means the adulterous man was caught as well. While trying to prove their own allegiance to the Law, these men fall drastically short of it: they have not brought the guilty man as well!

The underlying challenge here is nearly identical to other paradoxes and conundrums with which Jesus was presented (Matthew 16:1; 19:3; 22:35; Luke 10:25; 11:53–54). If Jesus agrees to stone this woman, it will greatly damage His reputation for being a friend of sinners (Matthew 11:19). Also, it would probably give them an excuse to turn Jesus in to the Romans for breaking the law (John 18:31). On the other hand, if Jesus rejects the law of Moses, the scribes and Pharisees can write Him off as a heretic and prove their accusations against Him.