Believe it or not, 23.98 fps is the standard frame rate for “24p” video.
The reason goes back to the earliest days of color television. Black-and-white television had a frame rate of 30 fps (that is, 60 fields per second, with interlacing). When color was introduced, they had to slightly reduce the frame rate in order to add the colorburst signal without exceeding the radio bandwidth mandated by law (and expected by existing television tuners).
The frame rate is reduced by 1/1000 producing a frame rate of approximately 29.97 frames per second (30/1.001) or 59.94 fields per second (60/1.001). The slowdown is low enough that it is within the error margin permitted by TV tuners, so B&W sets have no problem syncing to color TV signals.
In the digital age, there is really no need for this, but despite that, digital TV broadcasts all use frame rates of 29.96 and 59.94 fps (which is presented to users as 30 and 60). This is probably for backward compatibility with NTSC and existing NTSC-based equipment, but you would think that they could have chosen 30 and 60 for HD broadcasts. Nevertheless, they did not, I’m guessing so they could reuse their existing hardware/software that is all designed for these frame rates. This means, unfortunately, that video editing tools that export to TV-compatible video (e.g. DVD and Blu-Ray, as well as for broadcast) all work at 29.96 and 59.94 fps. Video sources that are actually 30 and 60 fps must be converted.
Movies on film have always used 24 fps. In order to convert a movie for a B&W broadcast (at 30 fps), it is necessary to increase the frame rate to 30 fps. In its simplest form, 6 of each second’s 24 frames (that is 1/4 of them) are duplicated. In actual practice, it’s a bit more complicated, where image data from adjacent frames are blended using adjacent fields. The conversion process is known as the Telecine 2:3 pull-down.
Of course, in reality it is uglier than this because unless you plan on using an antiquated B&W broadcast signal, you really need to convert those 24 fps to 29.97 fps, not 30. The Telecine process takes care of this by slowing down the source frame rate by 1/1000 (producing a 23.98 fps source). The Wikipedia page provides a good summary of the process.
With a 23.98 fps source, you can use a 2:3 pulldown, increasing the number of frames by exactly 25% to produce the required 29.97 and 59.94 fps.
You may occasionally run across video files (especially older ones produced with cheap non-professional software) that captured a video signal (from broadcast, VHS, etc.) and didn’t take the 1/1000 ratio into effect, treating the signal as if it was 30 fps instead of 29.97. The resulting video ends up running slightly too fast. You won’t notice the speedup, but you will notice the audio drifting out of sync for all but the shortest clips.