A supermassive black hole (SMBH) is a large black hole, often in the center of a galaxy. A black hole is considered "supermassive" if its mass is on the order of millions (or hundreds of thousands) of solar masses or more, sometimes cited as 108 through 109 as typical. The largest observed as of 12/2012 is on the order of 20 billion solar masses.
Such large black holes are considered the energy source for an active galactic nucleus (AGN). Such a black hole has been detected in the center of the Milky Way by observing the tight orbits of stars around it.
There is a mystery regarding SMBH formation since the Eddington luminosity would seem to regulate their growth. Current SMBHs have enough time, but quasars at extreme redshifts suggest a power source that only an SMBH can provide, and they had very limited time to grow, and furthermore, it would seem that given the necessary growth, they would be visible from the thermal emission due to the high accretion.
A supermassive binary black hole (SMBBH) is two orbiting SMBHs. They are thought to result from galaxy mergers.
Regarding terms, SBH is occasionally used to mean SMBH, but perhaps more often to mean "stellar black hole". SMBH unfortunately might be used or read to mean "stellar mass" or "solar mass", but its use as "supermassive" appears pretty consistent.