Cold Wallet
A wallet whose private keys are kept on a device or medium that never connects to the internet.
Cold storage ranges from a consumer hardware device that signs transactions over a cable or QR code, to institutional deep storage where keys are generated in a secure room and transactions require several staff members and a documented procedure. Keeping the key offline defeats remote attackers, at the cost of speed: institutional withdrawals from deep cold storage can take hours or a full business day by design. Cold storage does not defeat every threat, since a user can still approve a fraudulent transaction on the signing device, and the physical backup can be lost, destroyed, or stolen. Most operators combine a small hot wallet for daily flow with cold storage for the bulk of assets.
In practice
Air-gapped signing passes an unsigned transaction to the offline device by QR code and returns the signed version the same way, so the key never touches a networked machine.
The common misunderstanding
Cold storage protects keys from remote theft, but it does not protect against approving a fraudulent transaction or against losing the physical backup.