Most notably, this patch fixes a number of relatively common in-game scenarios that have been causing the game to crash. It also improves the item-handling abilities of your character's Followers, ensures that proper gems can be found in higher difficulty levels and fixes an issue that would cause a player's controller to vibrate indefinitely.
As with all Xbox 360 patches, this latest Diablo 3 update will be applied the next time you fire up your online-enabled console. A full list of changes can be found on the official Diablo 3 website. Just ignore the bit at the top stating the details only apply to the PlayStation 3 game; apparently Blizzard has yet to update that particular page.