1990osu said:

I read in a book some time ago that 24 fps was decided on as the result of a variety of different tests- it was determined that it produced smooth motion but being slightly under 30 the strobing effect put the audience into an altered state. After lots of tests done at a variety of different frame rates, it was determined that 24/25 was the best format for narrative stories.

If I recall correctly another reason was the introduction of sound. That's whty the big switch happened between 1928 and 1930. With soundtracks on shellac records you had to sync 78 rpm to 24 fps (and it'd go out of sync because of missing frames), and with sound on film it was a good compromise between speed (cost) and sound quality. Obviously it's like magnetic tape, the faster it is, the more fidelity you can get out of an optical recording.