In every level of Donkey Kong Country Returns, there are either 5, 7 or 9 Puzzle Pieces. Many parts of the landscape that you can interact with will reveal puzzle pieces. Try pounding the ground near interactive elements, blowing out fires or at the leaves on plants. In some cases, collecting all of the bananas floating in a circle in the level will reveal a puzzle piece. Puzzle pieces may also be found in secret areas (which are in most levels in the game) in which there will be a challenge to collect bananas, banana coins and life balloons and a puzzle piece will appear. Some levels have two secret areas.
The importance of having puzzle pieces in a level is to unlock collectibles in the gallery. Collect all the puzzle pieces in a level and you'll unlock an image that goes in the image gallery. Collect all the puzzle pieces in a world and you'll unlock a diorama, which are 3D spinable models of a world (i.e. The diorama of the Jungle world could be Mugly chasing Donkey Kong up a huge tree, but it isn't). Puzzle pieces, if you collect every single one in the game, will help you on your way to completing the game.