Left Brain Right Brain would be better named Left Hand Right Hand, as the entire focus of the game is to help train your non-dominant hand to be as dexterous as your dominant hand (i.e. train you to be ambidextrous). If you can force yourself to sit through yet more minigames on the DS, ambidexterity may be an achievable (if not entirely fun) goal.
To get your non-dominant hand up to speed with your dominant hand, you play a series of minigame exercises that are focused on speed and dexterity.