Cold storage is a type of non-custodial Bitcoin wallet that stores your private keys on a device that is not connected to the internet. When you want to use Bitcoin, you must connect your cold storage solution to the internet so that you can interact with the Bitcoin blockchain. The extra step of needing to plug and un-plug cold storage devices is a security measure. That means that anyone trying to gain access to your Bitcoin will need to physically access your device. Many people put their cold storage wallets in a safe. Some may even set up a multi-signature wallet with multiple cold storage wallets serving as the private keys to access that wallet.
Cold storage solutions are the most effective way to store your Bitcoin safely, particularly if you are not interested in spending it.
Trezor, ColdCard, and Ledger are all types of cold storage wallets.