What does search by rank do?

Search ranking is a complicated process; we started with "standard" algorithms, but may have some subtle tweaks, and plan more in the future. (Like Google -- it's always changing.)

In simple terms, it's a measure of how similar the target "document" (an article in a book, in our case) is to the query. Now there's a big difference in document length and query length, but the basic idea is that you rank higher documents in which rarer query terms appear in higher frequencies. 

So if I search for 

the huge dog

you'll get a higher rank for documents in which "huge" and "dog" appear frequently, but the frequent appearance of "the" in a document won't promote its rank much, because "the" is not at all rare. 

If you want to go further, start with reading about "tf-idf" http://en.wikipedia.org/wiki/Tf–idf

Beyond that, every search engine starts introducing special hacks and tricks to improve ranking, by usually subjective criterica. (Search "pizza san jose" while you're in San Jose, California, and Google gives higher rank to pizza restaurants near year. Search for the same thing while in Costa Rica, and it'll promote San Jose, Costa Rica restaurants higher in the list, etc.)