Cold storage means the signing key never touches a networked computer. That can be a hardware-wallet used carefully, an air-gapped machine, or keys held only on paper or metal.
It defends against the most common loss: remote compromise. It does not defend against physical theft, fire, flood, coercion, or your own failure to test the backup, so the plan must cover those separately.
Practical test: before funding cold storage meaningfully, wipe the device and restore it from your written backup with a small amount. An untested backup is a guess, and people discover the guess was wrong at the worst possible time.
Related: hardware-wallet, seed-phrase, self-custody, hot-wallet