A cold wallet is a wallet that's not connected to the internet. It comes in different forms:

• Paper wallets( your private keys printed)
• Hardware wallets (devices which you plug to your phone/computer and transact from)
• Using a Desktop wallet like Electrum for example. You can have one wallet connected to the internet and another one in a computer that never touched the internet. You sign the transaction in the offline computer, and then broadcast it from the online computer.

And yes they're pretty secure. By order:

• Hardware wallets are probably the best, especially if you're going to be spending on a regular basis. Very secure and you don't have to worry about much (clipboard hijacking, malwares, etc.) because any transaction you make from ther software will need to be confirmed from the device itself (by pushing a button).

• Paper wallets are fine, but as soon as you spend from them, you should assume that whatever device you used to transact from has been compromised, therefore, it's not safe to use it anymore once you spend from it.

• A cold wallet with Electrum is fine, but less convenient (requires two devices, you have to do some extra work by sending the TXID while signed, etc.) and it also works with BTC only (or Litecoin for the Electrum-ltc version).