Google page rank is based on the number of in-links to a website and the quality of those in-links. There's a weighting mechanism, which is approximately logarithmic. For example, An in-link from a page ranked 6 is about 10 times "better" that one from a page ranked 5. There's also weighting for being a more unique link on a page, i.e. an in-link from a page with 3 links is much better than an in-link from a page with 100 links.

The exact weighting and algorithm is a Google trade secret and has been tweaked considerably since the first paper:

http://infolab.stanford.edu/~backrub/google.html

Therefore, the exact "science of page rank" is a mystery.

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