Ribbons and medals are commendations that you receive after fulfilling certain conditions during your gameplay, such as killing enemies or playing a specific game mode. Ribbons are awarded for specific activities while medals are rewarded for collecting a specific number of a particular ribbon and offer more fame as the reward.
You can find the list of ribbons and medals by tapping on your character's name and then tapping on Medals at the bottom of the screen. Some ribbons are intentionally hidden and you need to find out what is required for obtaining them.