This kind of search is sometimes called full-text search, or simply fulltext. It is a special type of search that looks for a given word or phrase using a so-called full-text search engine.
Unlike classic search, it does not search only in names and headings, but also in the content of the document itself (the HTML page). Search engines go through the words in specially prepared databases, which is how a result is obtained in the shortest possible time.
Use
Full-text search works by comparing the searched phrase or word with all the words in a given document. All pages that contain the searched phrase are then shown in the full-text search results. Advanced search engines can also display results by relevance, that is, similarity to the searched term, for example based on the topic.
Everyone surely knows full-text search engines. In the Czech Republic the best known are Seznam, Centrum and others, and worldwide it is Google.