A cold storage wallet is used for storing crypto assets where the private keys and access to the wallet are offline thereby protecting the funds from unauthorized access, hacks, and other vulnerabilities. There are physical devices, like Ledger’s Nano S or Trezor’s One, or simply something analog like a sheet or paper containing the private keys to the wallet. With the physical devices, the unit is connected to a computer to authorize transactions and generally has a passcode to gain access to the device itself. 

The security advantage of storing funds on a cold wallet is that they cannot be hacked unless someone either:

• Has access to your 12- or 24-word seed phrase (or written private key in the case of a paper wallet)
• Has access to your physical device and the device’s passcode