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The magic behind a search machine like Google, Bing, Yahoo, etc. is the algorithm. In Google the algorithm (PageRank named after Google Co-Founder Larry Page) analyses the graph of websites in the Google Index ("Coffein") to get the most usefull results.
But how do the websites get into this Index? This is done by Search Robots. A Search Robot starts on one site and looks for keywords (the website is now linked to these words in the Index) and moves forward through all the links on the page, where the keyword-search starts from the beginning.
The PageRank algorithm is very complex and has a lot of parameters. For example if a site is linked from microsoft.com (a site with a huge influence, cause lots of other sites refer to it) has a higher rank than a site that's linked from nobody-knows-this-site.to.
For more information especially on Google Search Engine visit http://www.google.com/insidesearch/underthehood.html
Thanks for that tidbit Zuck. I always thought PageRank was just the page rank. I had no idea that it was named after Larry Page. lol Nice bit of trivia.
His name fits good here, doesn't it! I just found a good graphic to visualize the effects of PageRank (http://upload.wikimedia.org/wikipedia/commons/f/fb/PageRanks-Example.svg). There you can see how links between sites has influence to their position in search results.