Similar to power-ups, medals help you with scenes investigation, but their effects last for a set amount of time, not just one scene. One type of medals disables special search modes, another gives you a chance to find useful items, and a third type increases the reward for successfully completing a level. Tap the image of a medal in your inventory or in the store to find out more about what it does.
The medal timer and the symbol are shown next to the player's avatar in the top left of the window.