When we say "character development" we don't mean revealing his backstory or meeting his family, we mean that his mettle is being tested. Whatever seemed like a good idea at the inciting incident is now unattainable, lost, or destroyed. The character will be in very different circumstances. He is fighting his own desire to quit, or if he is normally on the losing end he will feel like the story is over and he has failed, again.
Relations are strained, and this also changes the emotional landscape. Power dynamics change. Friends turn out to be other than they seemed. Mentors die, loved ones and support systems are are left behind. These are all personal disruptions that are (hopefully) tied into the inciting incident, the character's shifting circumstances, or the end-goal.
The middle of the story finds the characters we've started to know and understand, forced to improvise and compromise. They will either need to discover a new perspective on the situation or themselves.
But, not every story is about a "flawed" personality who needs a Freudian realization. If the character is a super hero or a master spy or a clever reporter, the middle is where he "does the thing he's good at". Kurt Vonnigut has a funny talk where he uses Cinderella as a foil to modern plotwriting – the middle is where Cinderella goes to the ball. The middle is when James Bond gets under the skin of the villain, and Superman saves the day. For iconic characters, this is when they get to be the icon.
Orson Scott Card described a MICE Quotient for storywriting. The C is for Character, but the other letters are story factors that should also be progressing. Milieu is worldbuilding, Idea is "what if…?", and Event is the world-out-of-whack (disaster, war). Similar to Character, this development shouldn't just be reveals and backstory, but should be actively unfolding conflict. The Milieu has gone from odd to dangerous. The Idea has revealed unforeseen complications, and ramifications from the Event are starting to cripple progress.
All of these should feedback into the Character development by creating new aspects to his situation – not always hardship or setbacks. Unexpected success can test the character's mettle and strain relations, too.