The recipient has to grant you a specified amount of trust, which in essence means he is extending you credit in the specified amount. The balance between the two of you starts out at zero. When one person makes a fiat payment in Ripple and the balance of the trust line is sufficient to allow it, Ripple will make the payment by adjusting the balance. If it is insufficient, it will try to adjust balances they have with third parties they both trust, such as gateways. If that is insufficient, it will try to involve even more people according to the trust graph. If the sender's wallet balance plus any unused trust lines is insufficient to cover the payment, it won't be made. If it is sufficient, it might still not be made if there are too few paths between sender and recipient and all relevant trust lines are maxed out.

Your total wallet balance is the sum of everything people owe you minus the sum of what you owe other people. Ripple does do the netting for you, but you do still have to periodically settle with people you have a trust relation with. Clearly, these trust lines in Ripple should correspond to real trust between real people in the real world. You should never grant more trust than you are comfortable losing.