BCs basically come in two types: Jackets, in which the air bladder wraps around the front of the diver, and back inflate, in which the air bladder is entirely behind one. The backplate and wing setup is a type of back inflate BC. As such, it is a BC, and functions precisely the same way -- you add air to compensate for lost buoyancy with compression of your exposure protection, and to compensate for the gas you intend to use. You exhaust gas as you ascend.
So why do we wax rhapsodic about backplates and wings? First off, it's a very simple system. One has the plate, which can be stainless steel, aluminum, or plastic. It's attached to the diver with a harness, which can be simple 2" webbing, or can have releases and padding and all sorts of "improvements". It's also attached to an air bladder, which lies between the plate and the tank. The bladder can be U-shaped, or doughnut-shaped, and can vary in size and lift for light, tropical diving, for single tank cold water diving, or for doubles in various environments. Everything is modular, so you can put together the rig that works for the diving you do, and you can change one component to dive different setups or in different conditions.
Secondly, the stainless steel backplate is five pounds of ballast. Many standard BCs have padding, which makes them buoyant. If you are wearing two or three pounds of ballast just to sink your BC, switching to a BP/W may allow you to drop 7 or 8 pounds off your belt. You can also purchase a weighted STA (single tank adapter, needed for some setups because BP/W rigs were originally designed for double tanks) or, for DSS plates, weighted plate to bolt on, to replace even more of your belt ballast. In some cases and conditions, you can easily construct a BP/W rig that doesn't require a weight belt -- but it may also leave you with no ditchable weight, something you need to consider and decide if you are comfortable with such a setup.
Thirdly, having the weighted backplate on your shoulders tends to make achieving and maintaining horizontal trim easier, especially for people in cold water. This is one of the reasons that people get excited when they switch, although in many cases, the same weight balancing is possible with other BCs, if you use camband weights or tank neck weights, or your BC has well-located trim pockets.
Fourth, and a big reason why I like backplates, is that the rig keeps the tank absolutely quiet on your back. I have been watching open water students in jackets, and no matter how well you cinch them down, the tank is still able to slop around some on their backs, and it creates a challenge for people who haven't built the habits of balance that we all develop with time. My first dive with a backplate sold me instantly -- I was so relieved to feel stable.
As far as a photograph, here you go: