While "midcore" itself is not a new word, the term "midcore content" is one that seems to exist basically entirely within this game's community, and after reading pages and pages of forum posts and reddit threads about it, it refers to, as best as I can tell, "unicorn" content that is:

-- Long, requiring weeks or, preferably, months to complete

-- Just difficult enough to not be completely brain-dead, but not difficult enough to introduce a non-trivial risk of failure or involve personal responsibility to other players

-- Consistently rewarding

-- Fun

So basically casual content, but less crappy then the casual content we have now. Or, in other words, "I wish FFXIV were a good game for non-progression raiders." It is not, sorry. I wish it were, but basically all discourse from the last couple years points to the fact that people are just clinging on because they can't imagine not playing the game anymore, despite the fact that it isn't fun for them.