Quoted for Emphasis
Quantum Ion Drive, reward from Nyms Starmap Quest
A Quest is a task given to you by an NPC. Usually after you complete the required steps, you receive some sort of reward (experience, credits, or maybe even an item of great worth).
A quest in the strict sense, is a task recorded in your Quest Journal; as distinguished from a Mission. Quests can be simple ("talk to Frank in Hobokin, then return to me") or more complex ("collect information from these three sources; after reporting back, collect more info from this other source; report all this to my boss").