From the recruiting presentations I saw while at university: they primarily do large scale information grouping and retrieval. It seemed like their systems (at least the ones they were public about while trying to recruit from undergrads) were aimed at taking large numbers of random facts about actors ("this person has made a lot of phone calls to this person", "this person was seen in place a", etc.) and making them all traversable as a sort of information-visualization graph. It seemed likely rather math-y and very interesting.

So basically the "information collation and noise reduction" part necessary for any mass surveillance system to be actually useful.

Palantir for doctors would basically just be Palantir with people's medical information and medical research plugged in, and maybe family connections, instead of "Person a called person b", "Person b has known terror connections.", etc.

As a former user there are two primary features: Network Graphing and Concept Linking

The big feature is basically tagging words or phrases in a source document - like a medical report in this example and then linking it with other documents with the same tags to reveal associations.

Generally it kind of just gives you a nice visualization of what you already know. However in a networked environment when you "expand" your links by ingesting other people's tags and nodes that is where you get some interesting links and patterns.