8-bit gains its name from using from the memory addresses or integers which can be no more than 8-bits wide (or 1 octet). 8-bit also describes a time when 8-bit processors were the norm, often referring specifically to third-generation consoles (Nintendo Entertainment System and Sega Master System) in the 1980s.
The first widely distributed 8-bit processor was the Intel 8080, designed by Federico Faggin and Masatoshi Shima (both of whom had previously invented the first microprocessor, the 4-bit Intel 4004). Released in 1974, the 8080 was soon used for the arcade game Gun Fight in 1975. The 8080 also gained notoriety with computer hobbyists from the late 1970s to 1980s.
By the mid-1980s, arcades had moved on to using 16-bit processors, with computers and consoles following suit in the late 1980s. The 8-bit era eventually came to an end by the early 1990s, with the rise of 16-bit processors.