In many machines it involves a set of magnetic clutches which hold the cyclic in a given position, but can be moved against springs as one of the other posters pointed out. Press the button, the clutches release, release the button, they reengage to whatever position you've moved the cyclic while you were holding the button down. A beeper trim (or coolie hat or chinese hat) will slowly reposition the clutches in whichever direction you move the hat.
Many folks believe for most smooth flying that best practice is to press the trim, move the stick, release the trim, repeat. If you move the stick then press the button, the stick will tend to jump. There are many arguments on this in different flight regimes and once you wade into that swamp you're never coming out. There are also differences between systems on different machines, with the more complex machines being well... more complex.