My understanding is that every bitcoin contains the entire block chain which contains a record of every transaction made in the network.
A transaction is basically three pieces of data: private key signature of the sender/payer, public key of the receiver/payee, amount of bitcoins.
The blockchain is very difficult to counterfeit, so theoretically a site like MyBitcoin.com can't actually 'control' your wallet or transfer all the bitcoins to themselves, at least without all the private keys of their depositors.
A transaction is basically three pieces of data: private key signature of the sender/payer, public key of the receiver/payee, amount of bitcoins.
The blockchain is very difficult to counterfeit, so theoretically a site like MyBitcoin.com can't actually 'control' your wallet or transfer all the bitcoins to themselves, at least without all the private keys of their depositors.