A backplate is a device made of metal or plastic to which is attached webbing for a harness and to which one's tank/s is/are attached.
The tank, or tanks as the case may be, is/are attached by either an STA (single tank adapter) or with tank band/s or both. Double tanks are connected by metal bands which are subsequently attached to the back plate with bolts that pass through the back plate and are secured with wing nuts.
A wing is a bladder of air designed to compensate for buoyancy at depth and for flotation at the surface. It's basically the same as the air bladder on a B/C (buoyancy compensator).
The wing is generally designed for use with a single tank or a double tank.
If you need further information regarding this gear configuration it can be found in the "Hogarthian" forum.