A great family-friendly exercise of the mind, and not a bad party game either.
The game is adapted from the DS version of the same name. You enroll your Mii in an academy and take part in a series of games that test five areas of your psyche: visualization, identification, memorization, computation and analyzation. But you can't just simply know how to solve the problems; you have to solve them as fast as you can. Only in this way does the game keep track of your personal development through use of a chart and some rankings. Don't take any of it personally. Just because the game ranks you as not-so-smart doesn't necessarily mean you're dumb in real life. The game encourages you to practice thoroughly to improve your brain cognition and all that whatnot, but unlike the Brain Age games, you're not required to play it every single day. It's more or less a casual thing, and it's not like your brain is going to deteriorate the further you're away from playing it.
But why would you NOT want to play this game? The mini-games are really fun and quite challenging to the mind. My friends and I play it on weekends--sometimes over Super Smash Bros. Brawl (SOMETIMES!) and Mario Party 8. It's really a neat exercise of human logic, intelligence and quick wit. Few games on this or any other console deliver the kind of experience Big Brain Academy: Wii Degree does.