8 Bit music is named after the sound processes that were used in the earlier eras of gaming, specfically around the early 1970s. The usage of 8 bit music at the time were for video game consoles like the atari 2600 and Commodore 64. The process of creating music for these consoles were using computer chips to synthesise the music themselves.
Following up in to the 4th generation of consoles were the start of Sega vs Nintendo. Nintendo games on the Super Nintendo too advantage of the new computer chips used for even higher quaility music and sound bits.
Even later in the future the 32-bit sound chips were developed and used for the GameBoy Advance Systems. The music was ran through a compressor that allowed synthized music to sound extremely close to their reworld counterparts, one of the more notable examples would be the pokemon series Ruby/Sapphire/Emerald with their iconic trumpet sounds.