Paper (and wood like the OP is offering) wallets are just another way to store BTC.  There are any number of services out there that will allow you to create, or will create for you, such a wallet.  You can print them from your home printer, burn them into wood, engrave them into metal, or just write them down by hand on a piece of paper.

Any wallet, be it paper, wood, metal, or electronic consists of two important parts: a public key and a private key.  The public key is what you give to other people so they can send you coins.  The private key is what allows you to access those coins and send them to others.  Think of this kind of like your bank deposit box.  Your bank will give you a key to open the box and deposit things.  Only they have the key to open it from the other side and retrieve the deposits.

If you go to blockchain.info, they've got a pretty decent tutorial.  Check it out here: https://blockchain.info/wallet/paper-tutorial