I've read the paper on CIRCA and can see how it would be able to interpret the gist of a document and pigeon hole it as "that's about whatever". But I'm having trouble understanding how it could say "that's more about whatever than this other document." The following is what I think might be the simple explanation. Please feel free to tear it apart with vitreolic postings.
Assuming a technology closely related to what is described in the CIRCA paper is what is now being used and reassessing my analysis of pages that are at the top of SERPs. I would say that the new algo seems to "like" pages that are about the broad context of the subject searched for and which contain the actual search term to only a small extent. In other words it seems to be more sure that something is about blue widgets if it is also about blue widgetting, green widgets and the study of advanced widgetology. This may change over time but at the moment putting blue widget in context seems to be most important based on my very small sample.
Then it seems to rank the pages by PageRank (or backlinks but there is a strong correlation between the two). So CIRCA decides what a document is about and PageRank (or backlinks) decides how important it is in relation to other pages that are pigeon holed as being about that thing.
CIRCA may also have some input in ranking in this way. It may look at the pages that are linked to by the page in question and if they are about the thing in question then this helps the strengthen the context of the page being ranked. In other words a page is more about a thing if it is linked to pages that are about related subjects to that thing. It may be that being related to is better than being the same.
Someone mentioned how it might filter out pages that are too much about a particular topic as being spam. I'm going to read back to see if I can find the post that refers to it but if anyone has more info on this please share it.
On page 5 of the CIRCA paper they give the example of "bears witness", suggesting there are two meanings of this expression. Of course there are at least three. My favorite is "Bears witness picnic ground incident, Booboo and Yogi seen running into the woods." ;)