What query fan-out means
The name describes the movement: one query goes in and several come out. In classic search, a person typed a string of text and the system returned a list of links ranked for that string. With AI-generated answers, that intermediate step is no longer a single one. The system interprets the intent, formulates on its own the supporting questions needed to answer, and retrieves documents for each one of them.
Two similar things should be kept apart from it. It is not the synonym expansion search engines have applied for decades, because there it was still a single search with lexical variants. Nor are they the suggestions that appear below the result, which are offers aimed at the user and not queries the system has already run. In fan-out the derived searches are genuinely executed, and the answer is composed from their results.
The practical consequence changes what you are optimising for. Your page stops competing for the phrase somebody typed and starts competing for a set of derived questions that nobody ever typed. You can be the first result for the original query and still not be cited in the answer, because the citation is decided in the sub-queries.