When you do a search, you can sort the results bibliographically alphabetical or by “rank”. What is Rank?
Rank refers to the search engine’s “best guess” as to the relevance of the result to the search you specified. The exact method of ranking used varies a bit depending on the search. In its most basic level, when you specify a single search term, rank looks at the density of the matches for the word in the document, and how close to the beginning of the document they appear as a measure of importance to the paper’s topic. The documents with the most matches and where the term is deemed to have the most importance, have the highest “relevance” and are ranked first (presented first).
When you specify more than one term to appear anywhere in the article, the method is similar, but the search engine looks at how many of those terms appear, and how close together they appear, how close to the beginning of the document, and can even take into account the relative rarity of the search terms and their density in the retrieved file, where infrequent terms count more heavily than common terms.
To see a simple example of this, search for the words (not the phrase, so no quotes):
Look at the density of matches in each document on the first page of the hits. Then go to the last page of matched documents, and observe the density of matches within the documents.
A more complex search illustrates this nicely with a single page and only 15 matches:
counter*tr* w/25 “liv* out” w/25 enact*
There are a lot of word forms and variants of the words (due to the * wildcards) above that can match, but the proximity (w/25) clause limits the potential for matching. What’s interesting here though is how easily you can see the match density decrease as you view down the short list.
The end result of selecting order by rank is that the search engine’s best “guess” as to which articles are more relevant appear higher on the list than less relevant articles.