A "hot wallet" is an account controlled by a computer program that holds the keys. It can make transactions in real time, but if a hacker gains access to the computer on which the program is running, he can steal the keys, and therefore the balance.

A "cold wallet" is an account for which the private key is stored offline, either on paper, in the brain of a person, or on a device like a Trezor. Since the private key is not online, it is theoretically impossible to hack a cold wallet.