To generalize, I would consider any difficult yet solvable (in the near future) problem - that upon solving would ultimately raise some standard of living - to fall into the "important problem" category. And I would also assume, from my own experience, that these problems are either presently unsolved or their current solutions are less than adequate; and producing an optimal answer would be extremely satisfying to the point of feeling like life as an engineer/contributor to society is one step closer to completion.

Conversely, it might help to examine "unimportant problems", ones that might be too monotonous or easy. Or maybe solving them doesn't quite scratch an itch. But in solving them, you know you're one step closer to achieving a greater goal.

So with that said, what problems do you consider worthwhile? What are these "important problems" we keep reading about?

Edit: I should have been more clear and mentioned where I see the term come up most. It seems to be mentioned almost weekly on various startups' blogs, most of which are geared towards web apps and the like. It would be interesting to discuss the non-obvious "important problems" from hackers' perspectives.