Here's my take; I'm sure there are other, better answers. (community wiki?)
On the one hand, you could ask a question that isn't very meaningful (e.g. why is 2 the only even prime), while on the other hand you could ask a question that in all likelihood you'll never be able to answer (e.g. describe explicitly the group of diffeomorphisms of a given manifold). The trick is to shoot somewhere in between, to find fruit hanging high enough that it's interesting and deep but low enough that you actually have a fighting chance.
Another (related) interpretation is that there are certain questions that have motivated a whole lot of fascinating research and discovery (why isn't there a quintic equation, what are the maps between spheres up to homotopy, are there or aren't there an infinite number of twin primes, etc.), and it takes a good understanding of the meta-structure of the field of mathematics and the way it progresses (or perhaps occasionally a blatant disregard for that meta-structure!) to hit upon such questions. Anyone can plug away through book after book, but it's as least as important to try to come to grips with the bigger picture.