Here's a link to an excellent, thorough explication of 3:2 (or, more correctly 2:3) pulldown:
3:2 Pulldown Explained
Briefly: The function of 3:2 pulldown is to enable conversion of 24-frame-per-second film to 30-frame-per-second video. Since our longstanding TV system is interlaced, that means converting to 60 fields (2 interlaced fields per video frame) per second. Since 60 is not an even multiple of 24, the solution is to use the first film frame for the first two video fields, the second film frame for the next three video fields, the third film frame for the next two video fields, and so on. This works well, although it introduces an artifact called "judder" to horizontally moving objects, since they are, in effect, speeding up and slowing down from frame to frame.
Now, this is all ducky so long as the display is interlaced, but what if you want to make it progressive? Current progressive-scan sets put up 60 frames per second, so 60-field-per-second interlaced video must be converted to 60-frame-per-second progressive. The easiest way to do this is simply to combine the first and second fields from the interlaced source into a single progressive frame, scan that frame twice, then combine the next two fields, scan them twice, and so on. But if you do this with material that has been converted from film, you wind up with some video frames that contain fields originating from different film frames, which can look pretty awful.
So to do the de-interlacing correctly, it is necessary to detect 3:2 pulldown when it is present and undo it during the de-interlacing process to ensure that film frames match up to video frames. Then it has to be reapplied to the assembled frames so that you wind up with 60 frames per second (first two video frames from the first film frame, next three video frames from the second film frame, next two video frames from the third film frame, and so on) instead of 48.
So that's what it's all about. Whether 3:2 pulldown compensation should be applied is strictly a function of whether the material being displayed progressively originated on film or on video.
Incidentally, this means you don't need to worry about this if the display is interlaced.