In plain terms
SEO helps a page rank in a list of links. AEO helps a page give the answer itself. A page written for AEO puts the question near the top and answers it in the first sentence or two, then backs the answer up with real detail from the business.
GEO (generative engine optimization) is the closely related idea of being mentioned and cited by AI assistants. In practice the work overlaps, which is why we treat AEO and GEO as one area.