A Monero account, or wallet, stores the information necessary to send and receive Moneroj. In addition to sending and receiving, the Monero Wallet software keeps a private history of your transactions and allows you to cryptographically sign messages. It also includes Monero mining software and an address book.
The term "hot wallet" describes a Monero account which is connected to the Internet. You can send funds easily but security is much lower than a cold wallet. Never store large amounts of cryptocurrency in a hot wallet!
A cold wallet is generated on a trusted device or computer via an airgap. If the device is to be reused, the data storage should be securely overwritten. As soon as a cold wallet is connected to the Internet or its mnemonic phrase or spend key is entered on an Internet-connected device, it's no longer "cold" and should be considered "hot".
A Monero paper wallet can be generated by downloading the source code of https://moneroaddress.org/. Verify the signature of the code on a trusted airgapped device. Create the wallet and print or store it on the media of your choice.
Monero accounts and paper-wallets can be stored on any media - paper, USB drive, CD/DVD, or a hardware wallet device (none available for Monero as of June 2017).