The reason Meta Knight has been banned is basically because he's amazing in every single aspect of the game, and has no real weaknesses.
Recovery and Gimping
Meta Knight's recovery is hands down the best in the game: He has 5 jumps, a glide, and even after all that he can use one of his specials to recover. Add in his very good aerials, and a good MK player should never be gimped (that is, knocked away to where they cannot recover), ever.
On the flip side, Meta Knight is one of the best gimpers in the game, as due to his recovery he can go anywhere, and his down air has good range, power, and sends the opponent back at a downwards angle.
Although Meta Knight does not have a projectile, once he has a significant lead, he can be almost impossible to hit, as he can just run away from the opponent and use his high priority high range quick attacks to make it very difficult for them to hit him until the timer runs out. The most infamous form of this would probably be planking (grab a ledge, drop down, use two up airs, and grab it again), which is nigh impossible for some characters to get around (and until recently was thought to be nigh impossible for most characters), and in fact was a big reason in why tournaments added a ledge grab limit for matches, to prevent Meta Knight from timing out the clock in such a way.
No bad match ups and overuse
Meta Knight's worst matchup in Brawl is another Meta Knight. The official matchup chart has only three other characters that go even with Meta Knight, and many characters he beats really really badly. This is further aggravated by the fact that in tournament play, half the opponents you'll face play MK. For example, there's only one really good Pikachu player (ESAM) at the moment, and Pikachu is pretty high tier. There's a ton of Meta Knight players (M2K, Ally, Anti, Sebrik, …), and it's rare for a national tournament NOT to be won by a Meta Knight.
So to summarize, Meta Knight is banned because he's broken to the point where he's used far more than any other character in tournament play, has no bad match ups and only a couple (arguably) even ones, as well as multiple broken aspects (his planking, as well as the infinite dimensional cape glitch) that require their own rules to prevent him from being even more broken.