What does John 1:21 mean?

Here, John the Baptist's interrogators (John 1:19–20) ask about specific Old Testament prophecies. The Baptist does not claim to be a particular figure, either the return of Elijah (Malachi 4:5), or the prophet whom Moses predicted in Deuteronomy 18:15. The only claim the Baptist makes for himself is a fulfillment of Isaiah 40:3, which he states later (John 1:23).

It's important to note that the religious leaders are constantly asking questions about their pre-conceived notions. They don't ask the Baptist to explain himself until after they've run out of their own ideas. This is a common trait, even today, in those who are resistant to the gospel. Their first instinct is to criticize, assume, and point fingers. At some point, when all those poor ideas are exposed, there is nothing left to do but ask what the gospel really means. Even then, as this passage shows (John 1:22), that interest is often aimed at nothing deeper than getting the conversation finished.