A bitcoin paper wallet is simply a public and private key printed together. As the name suggests, paper wallets are usually made out of paper, although free bitcoin paper wallet they could also be made of plastic or any other substance on which information can be durably printed.
Some paper wallet services have a nifty design that you can cut, fold and seal, making them a lightweight and relatively secure form of storing bitcoin offline. You send your bitcoin to the public address displayed on the wallet, and then store it in a secure place. They are not within the reach of hackers, and your bitcoin are never trusted to a third party. As long as the paper wallet is secure, your holdings are secure. But, therein lies the relative lack of security.