A cold wallet is an offline wallet for storing your BTC. It is a type of wallet stored on a platform which does not have access to the internet. This is because access to the internet leaves the wallet and it's funds vulnerable to hackers and unauthorized access. Thus the cold wallet protects you from such weaknesses.

When the wallet has access to the internet and is as such, vulnerable to all the things mentioned above, it is called a hot wallet. Every wallet has a private key. This private key is a jumble of alphabets and numbers, most probably randomly generated, that must be used to access the wallet address. The wallet address on the other hand is also a line of alphanumeric characters that is required for transactions. It is imperative that you keep your private key a secret.

So basically, a cold wallet is an offline BTC wallet and a hot wallet is an online BTC wallet.