I know this sounds really stupid, but I need to understand one thing about paper wallets. I understand that they are created offline for safety reasons, and that the private key never contacts the internet until the funds are to be used...but if it is completely offline, how is it that you can send bitcoins to wallet using the public key in the first place?
Because what you're storing is the private key it enables you to sign the transaction necessary for you to spend the coins from the associated address. Hence, while everyone knows and can send money to your address, no one can spend it without the private key which only you have and is safely stored offline.
In layman's terms, what you are storing offline is the proof that you own the Bitcoins, so when they are sent to an address you can effectively 'claim' them as yours. I'm not too sure if I explained it properly so don't hesitate to ask more questions.