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. A data unit of 8 bits is commonly called a byte (although the precise name is an octet), whereas a unit of 4 bits (a hex digit) is sometimes referred to as a "nibble".
The first widely adopted 8-bit microprocessor was the Intel 8080, being used in many hobbyist computers of the late 1970s and early 1980s, often running the CP/M operating system. The Zilog Z80 (compatible with the 8080) and the Motorola 6800 were also used in similar computers. The Z80 and the MOS 6502 8-bit CPUs were widely used in home computers and game consoles of the 70s and 80s. Many 8-bit CPUs or microcontrollers are the basis of today's ubiquitous embedded systems.