First: Its a minimalist system. It consists of a metal (usually) plate, either Aluminum or Stainless Steel, a 2" webbing harness that goes over both shoulders, around the chest, and has a crotch strap to secure the bottom. Once on it "just fits"; nothing moves or shifts during the dive.
The wing is just a bladder for gas, really. You can get them in different sizes and lift capacities. This is nice, in that if you move from recreational to technical diving, you change ONLY THE WING - the rest of the setup stays, so you don't buy the whole thing over.
Its also EXTREMELY rugged - you might hole the bladder, and need to replace the webbing for the harness (a whole $20 or so), but the plate will outlive you.
There is a guy here on the board (FredT) that makes custom plates more cheaply than you can get the Halcyon ones for. Or check eBAY. Tough to get "screwed" on that deal, again, since its just a hunk of metal...
There are two major manufacturers of wings to go with the plate for recreational diving - Dive-Rite and Halcyon. Both are price-controlled to one degree or another. Halcyon probably has the quality edge, but they're more expensive.
The third piece for recreational diving, unless you use Halcyon's system (and sometimes even if you do!) is called an "STA", or single-tank adapter. This is just a piece of metal with the cam-straps; it bolts to the wing and plate (with wing-nuts) and has the cam-straps you're used to to secure the tank.
A BP+Wing is my preferred buoyancy control device; I've dove a jacket, a back-inflate BC (I own a Scubapro Knighthawk - thought highly of in that arena) and the BP+Wing. After diving the latter, I can't imagine using the other two - its VASTLY more comfortable and far easier to get trimmed out properly (horizontally.) Not to mention cheaper than all but the lowest-end gear...
They work GREAT for tropical diving. During the summer months we have bath water around here (mid 80s), in the winter (like now) its in the upper 50s to 60s. I love mine in the summer - when I switched to it my trim and comfort in the water went up tremendously.
The other thing is that it doesn't trap water in it, which is a big deal when you are climbing up a boat ladder, and finally, it breaks down easily into its components (no tools, in seconds - literally) for packing purposes if you're going to travel.
There ARE, however, people who don't like the feel or fit - which is why I say find someone with one before buying it. You need to get it set up right or it will be ungainly and difficult to get on and off, or be "floppy" (if its too loose). Its not a big deal, but it does have to be done.