An example of the stage info that appears above the board during a stage. The Score appears to the top left below the Stage.
The Score is the amount of damage dealt to the target Pokemon in a stage, plus 500 * moves/3sec left after clearing the stage. In most cases, a high score is not very important, as rank is determined by number of moves/seconds left. Players can use it to keep track of damage dealt so far during a stage. In Competitive Stages, players compete with their high scores to obtain rare rewards.