(Note: This write is limited to GM's small block engines, as it turns out I know nothing about the other manufacturer's small blocks.)
Originally introduced in 1955, a small block Chevy - sometimes abbreviated SBC - is a V8 automobile engine. (It is not necessary to specify that "small block" refers to the engine. This will be understood by other car guys from context.) There are actually a number of GM brands that use this block - Chevrolet is simply the most well-known - as well as a number of different displacements, ranging from 283 to 400. (Note: These are factory displacements. It's possible to bore and stroke SBCs out to 454 cubic inches, but this is done by starting with an aftermarket SBC-compatible small block.)
Although referred to a "Chevy", use of these engine blocks was not limited to the Chevrolet brand, and they showed up in Oldsmobile, Pontiac, Buick, and I beleive even Cadillac cars (although Cadillac tended to use GM's big block instead).
There are actually four generations of SBC engines. These are generally just designated with Roman numerals. There's also a relatively recent variation on the 350, the Corvette LS1 motor, that is made completely of aluminum, giving considerable weight savings. As far as I know, all generations use the same mounting points and general layout, there are a number of differences as to what brackets can be used to bolt on the various engine accessories.