The trusted transaction
One way to imagine this is to think of Ethereum as a large global bank holding all reserves. This would mean no other interaction would go on with any other banks. All transactions would be internal. As this is on the blockchain so no employees are required.
Ethereum contains all the accounts of the holders, and each account contains Ether - the currency of Ethereum. There is no physical transaction here. Account balances are just debited and credited.
In Ethereum the list of accounts and all balances is known as a state. Every transaction on the network can be seen as a state transition.
Contract execution
Contracts are executed when several transactions occur. In our bank model the contracts have accounts too as well as the account holders. They act like lawyer middle men.
We can always check that a transaction contract has been executed correctly by checking if the two state transitions took place. Once the initial transaction is done, one account will be depleted by XYZ Eth, then the contract account should increase by XYZ Eth. After this the contract account will deplete, and the recipient balance will begin to increase in XYZ Eth.
In our banking model, the account model holders are part of a transactional blockchain operation that is both trusted and secure. This is one of the joys of Ethereum ... amongst many others! For more info see the Ethereum White Paper
Eth/Steem on!