First of all, fret height and action are independent of one another. Where fret size does play into the "action" of a guitar is by having an effect on how much your fingers will come in contact with the fretboard wood as you play and bend strings. This can be a major playability factor for a lot of players.
Jumbo frets give you that almost "scalloped" feel to the fretboard... even with lots of pressure, your fingers or the strings will rarely touch the fretboard, unless you're really digging in and playing hard. Makes for easy bending and vibrato with a lighter touch. The main drawback of jumbo frets is that they're more difficult to crown accurately, and as they wear, the breaking point of the string over the fret can get thrown off because the worn crown will be wider and flatter. Accurate intonation can be harder to achieve and maintain with jumbo frets.
Medium frets are just that... medium. They're narrower and not quite as tall as a "jumbo" fret, but still give you a decent amount of material to keep the strings above the fretboard and to have decent longevity over the life of the instrument. You can get "medium-tall" frets that are almost as tall as a jumbo, but still not as wide, so you get the long wear and minimal fretboard drag of a jumbo fret, but they're a little easier to get a good crown on, and the intonation will remain truer, longer.
Small frets are either the itty-bitty mandolin- or banjo-style frets that can give you a super-slick feeling (think 1970s Gibson Les Paul Custom 'fretless wonder'). Lots of cheaper vintage guitars have very small frets... you feel a lot of wood when you play these guitars... some people like them, others don't. I find bending with low frets takes a lot of effort, because all of the bend has to happen in the lateral direction... there's no room to push down to make the string go sharp. They're also a pain to set up, because they'll be very sensitive to string buzz, and they wear out extremely quickly.