There are a couple of different types of exciters and they don't work the same way, by my understanding.
BBE Sonic Maximizer: This machine claims to work on the principle of "phase alignment" along frequency bands. That is, higher frequency sounds travel faster than lower frequency sounds and speakers are not able to compensate for that. The sonic maximizer, supposedly, delays the higher frequencies by a certain amount, or something, so they arrive at your ears at the same time. Personally, I think the whole idea is ridiculous, but they do certainly change the sound -- often in an unpleasant way.
Aphex Exciter: I don't know what the technology is here, but it seems to add a bunch of high frequency garbage/noise to the signal, which I don't particularly care for. Possibly useful if you're dealing with a really dull sounding source, but the sonic artifacts would keep me from using it.
There may be others, but that's the gist -- adding unnatural high frequency crap.