What does John 8:4 mean?

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

It is unlikely that the woman was caught "in the act" mere moments prior and dragged directly in front of Jesus. More than likely, this was a woman who'd been previously found out, and carefully chosen by the Pharisees in advance.

In the next verses, the Pharisees will point out the Old Testament law which required the death penalty for adulterers (Leviticus 20:10; Deuteronomy 22:22). What they will fail to mention, however, is that the law did not merely require that they stone such women, but that they stone both of the guilty ones. In other words, in trying to prove their own allegiance to the law, these men are falling short of it, because they have not brought the guilty man as well!

The challenge being issued to Jesus is more or less the same as other paradoxes and conundrums with which Jesus was presented (Matthew 16:1; 19:3; Matthew 22:35; Luke 10:25; 11:54). If Jesus agrees to stone this woman, it would greatly damage His reputation for being a friend of sinners (Matthew 11:19). It would also, more than likely, give the Pharisees something they can accuse Him of to the Romans (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.