Cold wallets are a safe way to store crypto currency. They do not connect to the internet and only contain the user's address and private key. They work with software installed on a computer. By contrast, a hot wallet, or a computer that stores your crypto in the cloud, can be hacked.
A cold wallet stores your private keys in a physically secure location. This means that if hackers ever get hold of your private keys, you won't be able to steal them. Cold wallets can be software or hardware, though they're most commonly implemented as hardware. They're typically USB sticks. The advantage of using a cold wallet is that they're secure against malware and other security risks.