This type of sound differs from other sound effects as it acts as a type of reinforcement for the player, indicating that they have performed a correct action or progressed within the game; they usually take the form of an upbeat sound or 'fanfare', sometimes even an applause. Here is an example from the Metroid series and another from the Zelda series.
Reward sounds by definition need to be meaningful and indicate some level of accomplishment. Other examples are the reward sounds given upon getting a "tetris" or collecting an orb in Crackdown. However, the noise that occurs when Mario picks up a coin or Sonic collects a ring would not be considered reward sounds, as these sounds are intended to be the feedback sound that indicate that the player successfully collected the objects and are frequent events that occur almost effortlessly during the course of play. A reward sound is meant to accompany a sense of gratification in the player and cannot be equated to a specific action within the game; it exists purely to reward the player.
The most abstract usage of the reward sound that isn't directly tied to a specific player action would be the one heard when their character levels up, which has become ubiquitously referred to as a " ding." Everquest originated and popularized the term to the point that the onomatopoeia of the reward sound has become a verb that indicates a player has leveled, e.g. "I just dinged 50!" Completely irrelevant of what the equivalent sound is in other MMOs, players will still refer to the sound and event as a "ding" even if the event sound could more objectively be better described as a "gong," "blip," or "whoosh."
Reward sounds have proven so successful that they've been integrated into the OS level of current generation consoles, with Microsoft and Sony having introduced "Achievement unlocked" and "trophy" sounds, respectively.