8-bit refers to the number of bits used in the data bus of a computer. It is the number of bits of data transferred on each read or write of the memory, and the number of bits used internally in the CPU to carry out processing.
Similarly, a 4-bit[?] CPU would process 4 bits at a time, a 16-bit CPU would process 16 bits at a time etc.
The Zilog Z80 and MOS Technologies 6502 8-bit CPUs were widely used in personal computers and game consoles of the 1970s and 1980s.