What does John 18:35 mean?

The question Pilate asks here is not meant to be subtle, or polite. He's already indicated that he's not interested in Jewish religious debates (John 18:30–31). History tells us Pilate had a reputation for cruel, overly violent governance. His remark, then, can be read with a sneer—even sarcasm. Coming from his lips, the term "Jew" is practically a slur.

At the same time, Pilate is not stupid. He clearly knows about Jesus' popularity (Matthew 21:1–11; John 12:12–19) but hasn't seen a reason to think of Him as a threat (Matthew 27:18; Mark 15:10). He also knows just how much the Jewish people, including the scribes and Pharisees, despise being ruled by the Roman Empire. For them to voluntarily bring Jesus here, for judgment, is extraordinary.

This makes Pilate's second question one of genuine curiosity. What would inspire people who hate Roman rule to bring one of their own, with demands for Roman judgment? John's account here is probably a shortened summary, but the accusation being made by Jesus' enemies involves sedition (John 19:12–15). Jesus' response (John 18:36) strikes directly at that lie.