"8-bit" is a term used to describe an aesthetic based on the video games of the late 1980's and early 90's. It developed out of nostalgia and assumed nostalgia for the video games on such systems as the Nintendo Entertainment System, and gained popularity because the limited nature of the sound and graphics capability on an 8-bit system allow a minimalistic representation. In other words, "less is more".
The technical term "8-bit" should not be taken over-literally. Much of the appeal of "8-bit" art is in the bright, fun and cartoonish nature of the era, not in the specific hardware capabilities of the Nintendo Entertainment System. Super Mario World, a 16-bit game for the Super Nintendo Entertainment System, could still be considered an "8-bit" game, especially by those who are too young to actually remember the difference between the Nintendo and the Super Nintendo.
Although graphics and music meant to mimic the lo-fi capabilities of the 1980s may seem frivolous, like much on the internet, there is some charming, if not great, art made from this premise. It will be interesting to see if "8-bit" music and art lasts after anyone can remember its original stylistic origin.