Performance
Some games use the cache to store data as you play. If the cache becomes full, the speed of writing and accessing this data slows down. Clearing the cache speeds up the game's access to the drive, and may fix some stuttering or slowdown issues with certain games.
Remove Game Updates
Clearing the cache removes all game updates stored on the drive. If an update works incorrectly or otherwise interferes with gameplay, you can clear the cache to revert the game to its original state. Note that you can't play a game online over Xbox Live unless you re-apply the update.
Remove Achievements
Clearing the cache also temporarily deletes any game achievements you have earned, in case you want to to start over and re-earn your awards. Since the Microsoft servers also store your achievement data, you can restore the deleted information by connecting to Xbox Live.