Why Learn z80?
While most computers today are 64 bit with Intel x86 or AMD processors, There are still many devices that use Z80 processors. Most notable of such devices are GameBoy, Sega Genesis and Handheld Calculators such as Casio and the TI-series. Several other consumer electronics devices such as MIDI synthesizers also have a Z80 processor.
But why 8-bits?
The Z80 microprocessor was designed in the 70's it's competitor was Intel's 8008. Most computers in the 70s were 8-bit.