They all taste bitter, but other than that, they're very diverse.
Bitters wouldn't even be a constituent group on their own, were it not for the fact that they act very reliably on our digestion.
It's, get a bitter taste on your tongue -> salivation starts (= the mouth juices up) -> the larynx and esophagus juice up -> the stomach juices up -> the pancreas and gall bladder are primed for food and release their juices in time -> the gut (= small intestine and colon) juice up.
Get a bitter taste on your tongue 20-30 minutes before each meal and watch things hum along at a smooth clip, without the gut bloat, cramps and gas you'd get from a sluggish digestion, or from eating fats with a slow gall bladder.
I've done a blogpost on bitters here, but I see that I didn't go into the "what do bitters do then?" at all. Oh well, better later than never, eh?
Related entries: Constituents - Bitters - Swedish bitters - Indigestion