Collections are composed of items you receive whilst harvesting crops or trees, feeding animals, exploring or visiting your "Builds." Collectable items are automatically added to their corresponding Collection.
In each Collection there is one rare item. This item will be the most difficult to find.
When you do find a rare item, it will complete the related Collection and a window will open up asking you if you want to exchange the Collection for your Reward now or later. In most cases, you would probably want to select "Later", because there are some Quests that require you to turn in a Collection for its Reward, or there are certain things (like ) that you don't need at that time.
The Rewards are different for each Collection, and the amount of the Reward you receive, depends upon how many stars you have.
A star is accumulated every time you collect a Reward six times. There are a total of six "skill - stars" in each Collection. Once you have gotten all six stars, you have reached the maximum amount of the Reward you can collect.