What is cold storage?
Keeping private keys on a device that has never been connected to the internet.
Cold storage covers hardware wallets and other approaches that keep keys offline, so a transaction must be signed on an air-gapped device.
Why it matters
It defends against the largest category of loss: remote compromise of an internet-connected machine. It does not defend against everything, and the gaps are worth naming. A hardware wallet does not protect you if you approve a malicious transaction on it — the device signs what you confirm. It does not protect a recovery phrase you photographed or typed into a website. And it does not help if you bought a tampered device from an unofficial reseller. Cold storage plus a carelessly handled recovery phrase is not cold storage.