Search intent is the underlying goal behind a query — what the visitor is trying to accomplish, which is often different from the words they used.
On a website, intent falls into a small number of recurring shapes: find a specific known item, explore a category, compare options, check a fact (a policy, a size, a spec), resolve a transaction (an order, a return), or get help. Each shape wants a different response format.
Treating every query as product discovery is the most common design error in site search. "Where is my order", "do you ship to Ireland" and "is this true to size" are not product queries, but they are typed into the product search box constantly — and returning a grid of items to any of them is a failure the visitor reads as "this site doesn't work".
Intent classification — routing a query to the right kind of answer before retrieving anything — is therefore a prerequisite for good results, not a refinement on top of them.