Fragments are pieces of special items, such as Special Buildings. They are offered as a reward during events or Daily Challenges. If you collect enough fragments, you can assemble the item in your inventory.
To complete one of these itmes you need to collect all fragments specific for that item. For example, in case of the Wishing Well, you'll have to collect 15 Wishing Well fragments. You can check your progress in the inventory:
Once you have collected enough fragments, you can assemble the item in your inventory:
List of Fragments
So far the following fragments have been released:
Shrine of Knowledge
Wishing Well Shrink Kit
Statue of Honor