"Mid-fi" is a term invented by those wealthy enough (or foolish enough, depending on the model) to buy super top tier headphones and who need to feel that this somehow puts them in a class above everybody else. It's a nonsense term, especially when things like the HD6x0/K70x/DT880, which were once unimpeachably hi-fi, have now been "demoted" a rung. Nobody with a straight face can tell you that any of the $1,000+ headphones are fully >$1,000 better than the best models in the so-called mid-fi range, and most people are very honest about that and admit that they're not. Not saying it's not worth it to eke out that last bit of performance or to buy something well made and stylish, but audio is always a slippery slope. The distance between "mid-fi" and hi-fi is far smaller than the distance between lo-fi and "mid-fi."
The way most people seem to use the term these days it's more to delineate price range than quality, but you'll get the occasional snobiophile (as Doc likes to put it
) who will say that mid-fi is crap. Haven't actually seen one of those in a while, though, so maybe that attitude is waning.
EDIT: Clarity