Quests are special opportunities for Homura, which can occur whenever someone mentions a goal that at least partially aligns with Homura's own, or at least isn't opposed. Some additional considerations may apply, per GM decision.
Quests give rewards upon completion, and may (but also may not) have penalties upon failure. Rewards include increases of reputation (usually with the questgiver, but sometimes others), experience towards related skills, and often some mystery rewards.
Quest rewards can grant experience for skills regardless of the prerequisites; however, such a skill cannot be raised to the SKILLED level.