In one article on his blog; T. Gowers talks about ''expository problems''.
For those too lazy to click that link, a quote of a quote:
Solving an open exposition problem means explaining a mathematical subject in a way that renders it totally perspicuous. Every step should be motivated and clear; ideally, students should feel that they could have arrived at the results themselves.
I'm sure that all of us can value good solutions to expository problems, and that all of us were sometimes really frustrated by some expository problems.
So, what expository problems do you know? What's that one thing in math you could never intuitively grasp? If you are a member of faculty, have you ever noticed some topics in your field which are particularly hard to get for your students (and you don't really get why)?
P.S. I'm sorry if this question is too ''soft'' for math.stackexchange, but I think it's really interesting.