Unfortunately, although frame rates appears like a fairly simple subject it can get pretty complex when you need to get into the guts of it. Some/Many NLEs try to simplify this area while still providing all the functions which may be required.
Simply: Pulldown is the act of turning TV/video into film or occasionally vice versa. Film is 24 individual frames per second. TV/Video does not generally use individual frames as such, it uses (interlaced) fields, where two fields are equivalent to one frame. The 2:3 and 3:2 pulldown means this relationship of 2 fields to 1 frame is deliberately changed in order to account for a different speed. Not using a pulldown will simply play the 25fps footage at 24fps, IE. Your footage will run 4.1% slower than you actually filmed it and the duration of your film will therefore be 4.1% longer.
Unfortunately, with the advent of HD video the situation has become more complex as not all the HD video formats use interlaced fields rather than progressive frames and also the nomenclature has become quite confused by manufacturers using oversimplified terminology for the benefit of consumers. For example, 24p can mean either true 24fps in the case of film or 23.976fps in the case of video.
To get the best 25fps to 24fps conversion, which is best here?
Changing/Converting frame rates should always be avoided, there is almost always a price to pay with picture quality plus it often causes serious problems with audio synchronisation. If there were one best way to achieve a conversion, there would be no need of any alternate choices/options. Which is best therefore depends on exactly what you want to convert to and what you want to use your converted film for.
The obvious first question you should ask yourself is, do you really need to convert your footage? What platform are you looking at which won't allow 25fps? If you're absolutely certain you do need to covert then your best bet is to spend some time researching frame rates, fields, film and video speeds, because to get the best results you're going to have to be able to answer questions such as, do you really want 24fps or is it really 23.976 you're after and, how are you going to deal with audio sync?
G