Okay. Bitcoins are stored in the blockchain. Every client on the bitcoin network has a copy of this blockchain. The only way to access these bitcoins is with the private key to which they've been assigned. These private keys are what's been stored in your wallet. This means that only you can access your bitcoins, provided only you can access your wallet. This is why having a wallet on a thumb drive is more secure, as it means only you can access your bitcoins. Compare that to using MyBitcoin. As they're the ones with the wallet now, they could ostensibly take everything you have (to which you've allowed them access).