Definition
Fan-out is the strategy a feed or notification system uses to get one producer's item in front of many consumers. Fan-out on write pushes a copy into each follower's materialized feed at publish time, making reads a single cheap lookup. Fan-out on read stores the item once and assembles each user's feed by querying the people they follow when they open the app, making writes cheap and reads expensive.
The two strategies fail in opposite places, which is why large systems run both. Fan-out on write collapses on high-follower accounts: one post by an account with ten million followers becomes ten million writes. Fan-out on read collapses on users who follow a lot of accounts and on read-heavy traffic generally. The standard production answer is hybrid — fan out on write for ordinary accounts, leave celebrity accounts to be merged in at read time.
How it comes up in interviews
This is the central decision in every news-feed question and interviewers expect the hybrid answer, not a religious commitment to one side. Name the read:write ratio that motivates the default, then name the celebrity problem and how you special-case it. Quantifying the fan-out cost with real follower numbers is what separates a memorized answer from a designed one.