It's not that part of a person's brain dies, but the brain cells in the brain die. The difference is, saying part of a person's brain died is like saying an entire hemisphere of their brain shut down. Anyways, the reason it happens is the lack of oxygen. Your brain needs to breathe, so by not breathing, you're robbing your body of oxygen, thus suffocating your brain, and when your brain suffocates, the brain cells die, just like you would if you suffocated for too long.