(See also Address bus)
A set of digital signals which, when taken together as a set of 1s and 0s (bits), specify a number in binary. The 'width' of the data bus (the number of separate signals you use) determines the number of different values you can transmit down it - on an 8-bit bus, you can send 28 (=256) possible values (the range is 0-255 inclusive).

In more general terms, this is usually what is referred to when talking about generations of computers, video games consoles, or CPU chips - 4 bit is extremely primitive, 8 bit is fairly archaic, 16 bit is pretty long in the tooth, 32 bit is not-exactly-cutting-edge, and 64 bit and up are (at the moment) where the action is.