Short answer: AEO (Answer Engine Optimization) means optimizing content so an answer engine —Google AI Overviews, ChatGPT Search— uses it as the direct answer to a question. SEO chases the click; AEO chases having your content be the answer, with or without a click.
An article optimized only for SEO might build up before answering, because the goal is keeping the reader on the page. An article optimized for AEO answers directly in the first lines, because the answer engine extracts that specific part to display.
When someone asks Google or ChatGPT something related to your book's topic, AEO determines whether your content is the cited source — a form of visibility that doesn't depend on the person clicking at all.