Completing collections are the focus of some quests. Each collection requires you to find 5 specialty objects, as well as gather a number of general collection items (e.g., ribbons, boxes, gloves, etc.). Once all of the items are gathered, you can exchange them as a set for a few rewards. There's no real point in doing collections just to do them; just focus on quests, because you'll get plenty of collection quests as you go along.
You get this achievement for completing 10 collections, which you'll probably finish around level 13 or 14.