I would comment on [Peitro's answer][2], but I don't have enough reputation;  for a marvelously-titled explanation of Google's Pagerank, see [The $25,000,000,000 Eigenvector][1].


  [1]: http://www.rose-hulman.edu/~bryan/googleFinalVersionFixed.pdf
  [2]: http://mathoverflow.net/questions/40454/practical-applications-of-eigenvalues-and-eigenvectors/40461#40461