Generically speaking, they are for developing one's character beyond what can normally be done by just playing normally and without GM intervention. Sometimes it can be for adding classes not previously approved, but that's not their sole purpose.
One might request a CDQ to track down the survivors of his family, if they still exist. Or one might wish to join a particular group, seek out a particular artifact, do research, and so on.
In short, it's things you'd like your character to do (within reason, of course) that require GM assistance.
CDQs are requested by players, and as such, players give the ideas on what they would like to happen. Now that doesn't mean that a CDQ will always succeed...because they won't. The player supplies the context and the goals, and the GM makes it happen, but success or failure is in the hands of the character and whoever else he/she invites along.
Make sense?
