I know someone that has an inflatable one and loves it. They're pretty simple, a thing is attached the the saddle and the vest. When you fall off the thing is detached and the vest quickly inflates, kind of like an airbag. The cord stretches while you ride and needs a certain amount of force to actually release, probably around 60-70 pounds. They're actually modeled after motorcycle safety vests, though I'm not 100% sure what they're made of I know they're hardy. However, they're very expensive and you need to replace the CO2 things every time the jacket inflates. For some people it's worth it, the woman I know who has one had a major fall that broke multiple ribs and I think damaged her spine, she's fallen in this vest without further injury to it, but if money is tight then this might not be a good option since the CO2 things are like $75 each.
BETA is the association who sets the safety standards for the vests. I believe it's the British Equestrian Trade Association.