I'm sure I've explained this to someone before, but I will explain again, from the beginning. Here we go...
24fps means 24 frames per second. This is the frame-rate that just about every movie (feature film) is shot at. This is partly because it has a "cine" sort of look to it. Basically film-makers use this frame-rate partly for it's "look". Probably though, the main reason why films are shot at 24 frames-per-second is simply because this is the frame-rate that has always been used for film. It is the traditional frame-rate for films.
While 24fps is the frame-rate that has always been used for films, tv has always used a different frame-rate. In the UK, standard-definition effectively has 50 frames-per second, but in an 'interlaced' format. This means that there are actually only 25 full frames, but they are split into 2 'fields' - the first field is made up of all the odd horizontal lines, while the second field is made up of all the even horizontal lines. So, this format is called 50i - the '50' refers to the 50Hz refresh-rate (or basically frames-per-second) and the 'i' refers to the interlaced nature of this format. As for American tv, they use a different frame-rate - 60 frames-per-second. Again, this is interlaced, so there are actually only 30 full frames, but they are split into 2 'fields' so effectively there are 60 frames-per-second. Predictably this format is called 60i because of it's 60Hz refresh-rate and it's interlaced nature.
Anyway, all tvs from the past and many at the present are designed to work exclusively at either 50i or 60i, or both. In the past, when films or other 24fps material has been shown on broadcast tv, it has been converted to suit the tv. For UK tvs, the process is fairly simple - the 24 frames-per-second film is sped up slightly (by 4% to be precise) to 25 frames-per second, and then converted to an interlaced format so it becomes 50i. This is not ideal because it is distorting the original film - the tone of the sound is raised by 4%, and a 100 minute film becomes 96 minutes. However, it does not cause problems such as 'judder' which I will explain later.
With region 2 (UK) DVDs, the same thing happens, ie the 24fps film is sped up to 25fps and then converted to interlaced format. This is done in a studio before being mastered to DVD at 50i - meaning 50Hz / interlaced. Most modern DVD players are capable of outputing a progressive signal (for suitable tvs ie flatscreens) - this is when the frame is shown all at once - ie one full frame as opposed to two interlaced 'fields'. The process of turning the natively interlaced content into progressive scan (called de-interlacing) is done in the DVD player itself in real-time - as the DVD is being played. As the frames are not split into two fields as they are with interlaced, there are 25 full frames-per-second instead of the 50 half frames. So, to make up 50 frames-per-second, each frame is simply repeated. The end result is the format called 50p.
With region 1 (US) DVDs, they have to output at 60fps to be compatible with American tvs. In order to convert 24fps content into 60fps a process known as 3:2 pulldown is carried out, again in the mastering studio. This involves some of the original film frames being shown twice, while others are shown three times. This is pretty complicated, so to make things easier to explain let's imagining the whole process being in progressive scan (even though really, it would be converted from progressive to interlaced and back to progressive which makes everything much more complicated, and we ain't scientists!). So from the original film frames, every odd frame (frame 1, 3, 5, 7, 9, etc) is shown 3 times while each even frame (frame 2, 4, 6, 8, etc) is shown only twice, hence the 3:2 ratio in the name '3:2 pulldown'. This produces an order of frames that goes like this:
frame 1,1,1,frame 2,2,333,44,555,66,777,88,999,10,10,11,11,11 and so on...
This creates 60 frames out of 24 frames. The problem with this method of conversion is that is is uneven - ie the frames are shown at uneven rates, some more than others. This is what causes the dreaded judder effect where the image literally judders when there is slow movement, such as a slow camera pan. However, when this process is done in a mastering studio, time can be taken and proffesional equipment used to to a pretty good job.
So traditionally, 24fps film material has had to be converted to be shown on tv, whether via broadcast or DVD or video. However, with new tvs coming out that are capable of displaying 24fps, in the pursuit of the ultimate in picture quality, which is what HD is all about, both the Blu-ray and HD-DVD high-def formats support 24fps. In fact, just about every high-def disc on either format is mastered to disc at the original 24 frames-per-second, and in progressive scan format. This is brilliant, as long as your tv is one of the ones that supports 24fps. If your tv does playback content at 24fps then it will most likely either double or triple every frame so 24fps turns into a 48Hz or 72Hz refresh-rate. So, high-def content at 24fps is great - it is exactly how the director intended, and is free from distortion and judder, as long as your tv accepts 24fps!
If your tv doesn't support 24fps, and there are many that don't, then you will have to set your high-def Blu-ray or HD-DVD player to output at (generally) 60p to suit your tv, and in order for it to do this it has to do a 3:2 pulldown, like in the region 1 DVD mastering studio, except this time it has to be done in real-time, while you watch your movie, and without proffesional equipment. The results are often quite, poor. The conversion introduces judder to your pictures.
So, while 24fps is great if you've got a compatible tv, if you don't then it can give you results that are worse than with DVD which has been converted to the appropriate frame-rate in a proffesional mastering studio. I think I have covered everything and I am extremely tired, but I hope I have been of some help to you. For more extensive and complicated info then go to wikipedia and search for "24p" or "telecine" or something like that.