It's the total amount of money passing trough the network.
But since bitcoin transactions work by sending "change" back to yourself this value is not that relevant. In most cases 90% of the transaction amount is sent back as change.
You spend the results of previous transactions. Each transaction can have multiple inputs and multiple outputs, so when you make a purchase, you select enough payments that you have received to cover the cost as the inputs of the transaction, and make the purchase price (to the recipient) and whatever is leftover (back to yourself) as the outputs. (I imagine software would take care of all the complexity; and whatever is leftover, typically 0.01, is given to the miners to incentivise them to spend the processing power to authenticate the transaction.)
This means that the Bitcoins in somebodies wallet is conceptually the list of transactions that have been made to them (that haven't been spent yet). It also means that a nice big graph can be made of how money is (or isn't) flowing through the system.
