Search engines are web-based software tools used in databases and on the Internet that search for records that match your request. In a catalog or index database, they search for specified fields (author, title, subject headings, etc.) in each record of the database. The interface represents a special kind of Web page where the user types in a query and in return receives a list of links to sites that include all or part of what was typed. ... full article

Once a query is entered, nearly instantly, the search engine will sort through the millions of pages it knows about and present you with ones that match the topic. The matches will even be ranked, so that the most relevant ones come first.
So how do crawler-based search engines go about determining relevancy, when confronted with hundreds of millions of web pages to sort through? They follow a set of rules, known as an algorithm. Exactly how a particular search engine's algorithm works is a closely-kept trade secret. However, all major search engines follow the general rules below. ... full article

Let's take a closer look at Google, since it's the most popular search engine.

There are two main parts to the algorithm Google uses. The first is its text matching system, whereby Google tries to find pages relevant to what the searcher has entered. The second and equally important part of the algorithm is of course the Google patented Pagerank™ system. ... full article