The Google algorithm can be broken down into two major groups of factors

On-page (keyword) factors. Keyword factors involve how, where and when
keywords are used. Meaning how well your website is optimized for your most
important keywords, and if those same keywords appear in your content and in links.
Keyword factors determine page relevance.

Off-page (link) factors. These include the quantity and quality of links that point to
your site. Link factors determine page importance and are related to Google
PageRank (PR). Links play a VERY important role in getting high rankings,
particularly for competitive markets.

Very simply put, Google finds pages in its index that are both relevant and important
to a search for a particular term or phrase, and then lists them in descending order
on search results pages.