Rainbow Islands Revolution is an update of the original game, Rainbow Islands. Unlike in the original, the main character, Bub, rides in a bubble, and the player has to guide him with the stylus, and draw rainbows with it as well. Therefore, the game uses mainly the DS's touch screen.
The player has to drag Bub around using the stylus. Contact with enemies or dangerous objects such as spikes causes the player to lose a heart. When all hearts have been lost, the player loses a life and must begin the level anew.
Source: Wikipedia, "Rainbow Islands Revolution", available under the CC-BY-SA License.