The plain definition
An AI hallucination is a false statement an AI produces in the same confident tone it uses for true ones. The content is wrong, and nothing in the wording tells you so.
Why it slips past you
You normally judge an answer by how it is written: clear sentences, specific details, a steady tone. Those cues tell you the reply is well-formed, not that it is correct. A hallucination passes every one of those cues, which is exactly why it is hard to catch.
A made-up book
Ask for a book by a particular author and the AI may give a title, a year, and a summary. The title does not exist and the year is invented, yet the reply is written exactly like a real recommendation. The description is a sensible guess about what such a book would be about, which makes the whole answer feel more solid than it is.
Both halves matter
A wrong answer that flags its own uncertainty is not the same problem as a wrong answer stated as fact. Hallucination means false content plus no signal of doubt.