This was not for you. It was for another poster.
your wallet is the privatekey.
..
The balance then is simply the sum of all transactions.
The blockchain that the clients download, is a history of all transactions.. that's why there's a worry about the size of that. The paper wallet doesn't hold an amount, it allows you access to the account - that is, it allows you to action change in that account, which is the same. You then think that you own something called a Bitcoin.. but your don't own some-thing, you own an idea - that idea has value and that idea is money in your account. Money is an idea, a confidence that tomorrow you can spend what you have today... it's simply a medium that people agree on exchanging.. and that then communicate wealth. Wealth matters; money does not.
To check your account you can put the public address into
https://blockchain.info/ Do not ever post your private key to an online website!
Some third party sites will store the private key for you; you will have a public address and a more traditional password - Andriod blockchain.info app does that - but that's not as secure because you are trusting that 3rd party.. blockchain.info is probably ok but still not as secure as d.i.y.
Of course. This is like "open sesame" situation. Any body who knows how to access it, can spend (or put) BTC on it. Thanks.