Fan-out happens because a single search query rarely surfaces everything a comprehensive answer needs, so the system decomposes the prompt - by facet, subtopic, or intent - and issues several retrieval calls, sometimes against different indexes or tools, before synthesizing one reply. The user sees a single coherent answer; underneath, multiple searches ran to produce it.
Fan-out matters for AEO because it multiplies the number of queries a brand needs to be competitive on: ranking for the literal phrase a user typed is not enough if the system also fans out to comparison, pricing, or review-style sub-queries where a competitor’s content is stronger. Tracking visibility for only the headline prompt misses where fan-out actually decides the answer.