Defeating NPC trainers and opening iron/golden chests give you collectibles which are a part of one of the various collections (sets) that you can exchange for certain items. Unlike Trainer Tokens, collectibles can be obtained from trainers even if you've already fought them once. The collectibles that the trainers drop also depends on the area where you are fighting them. For example, all trainers in The Southern Forest will drop leaves only.
Collections enable you to exchange them in return for common or uncommon items, by collecting all five objects in the set. In order to start collecting and exchanging sets, you first need to activate that collection by completing a quest for the particular NPC that unlocks that collection. Although you can exchange a collection only after you have unlocked it from its NPC, you can start collecting its items before you've done so.
At the moment, there are only 6 collecions that you activate in the forest areas. There are no new collections to be activated in the mountain and desert areas.
Leaves Collection: Unlocked by the girl in green at the top left of the area in The Southern Forest.
Maple Leaf, Apple Leaf, Dark Leaf, Clover Leaf, Oak Leaf = 1 Small Healing Potion
Broken Items Collection: Unlocked by the sweaty guy next to the nurse in The Deep Forest
Broken Potion, Broken Capture, Broken Tablet, Broken Telepad, Water Vial = 1 Small Fire Bomb
Fruit Collection: Unlocked by the NPC near the teleport pad in The Tangled Forest.
Orange, Pear, Lime, Strawberry, Watermelon = 1 Small Nature Bomb
Agate, Aquamarine, Emerald, Ruby, Diamond = 1 Small Water Bomb
Blue Mushrooms, White Mushroom, Red Mushroom, Swirl Mushroom, Purple Mushroom = 1 Medium Defence Potion
Sports Collection: Unlocked by the Dyed Trainer in The Wooded Forest
Sports Jersey, Football, Baseball, Tennis Ball, Bowling Ball = 1 Medium Attack Potion