This is the first part in what is now a three part series, with the second part available at 20 More Ways that Search Engines May Rerank Search Results, and a third part at Another 10 Ways Search Engines May Rerank Search Results. It may be time for a fourth part soon. (Added 2013-08-31)
Search engines try to match words used in queries with words found on pages or in links pointing to those pages when providing search results.
Often, the order that pages are returned to a searcher are based upon an indexing of text on those pages, text in links pointing to those pages, and some measure of importance based upon link popularity.