https://www.facebook.com/video/video.php?v=432864835468
Briefly, first_degree.php returns objects you're directly connected to in the graph, and if there's space a few machine-generated guesses at other good results. We preload these as soon as you focus the "Search" box at the top of the page, in the hopes of having some decent results to show when you start typing. The index field does, as the article inferred, represent our best guess at a ranking function on these first degree objects. The inputs to this ranking function explicitly do not include other users' behavior on the site. I talked a bit about our ranking function in this quora question:
http://www.quora.com/How-does-the-new-Facebook-search-engine...
Edit: To clarify what a lot of people seem to be wondering, visiting someone's profile does not affect the search results of anyone but yourself.