What does John 8:25 mean?

The Greek phrasing used in this verse is not entirely clear. The Pharisees might be asking this as a sincere question. They might be saying it as a rhetorical attack: "just who do you think you are, anyway?" Either way, Jesus' response goes to further support the Christian view that Jesus is not only God, but consistently presented Himself as God to others. Here, Jesus makes this very observation. He has been saying who and what He is since "the beginning" of His earthly ministry.

In the course of His teachings, Jesus will claim to have equal power to God (John 5:36), equal judgment to God (John 8:16), and equal authority with God (John 7:16–18). He will say He has been sent by God (John 8:18) and approved of by God (John 6:27). Jesus professes to be the one and only way to know spiritual truth (John 8:12), and that those who reject Him do not know God (John 8:47), and will die in their sins as a result (John 8:24). Earlier, Christ pointed out His miracles (John 5:36), the evidence of Old Testament Scriptures (John 5:39–40), and the testimony of other people to support His status (John 5:33). And yet, out of stubbornness and disobedience (John 8:43), the Pharisees claim to not know who Jesus is.

It's important to note that, at this point, Jesus does not offer additional proof or argument. This is a useful principle for modern Christians to keep in mind: at some point, those who ask for even more proof are not being honest. Those who refuse to accept what they've been given won't benefit from being given even more (Matthew 7:6). As Jesus will point out in the next verse, there is much more which could be said, but hardened hearts like theirs would make such efforts a waste of time.