What is cold storage?
Keeping your keys on something that never touches the internet, such as a hardware wallet. An online wallet is a hot wallet.
A payment is signed wherever the keys are. With cold storage the keys stay offline, on a hardware walletHardware walletA small device that holds your private keys and signs payments inside itself, so the keys never touch your internet-connected computer or phone. or a written backup, and only the signed payment crosses to an online machine. Malware on your computer cannot sign without them.
A hot wallet keeps keys on a connected device, which is handier for spending. Many people keep everyday money hot and savings cold.