PayPal handling with Simple Payments?
You need to process the payment. In your case you could mark that the invoice has been paid, maybe in storm or a custom table.  $payment should hold all the info about the payment that you need. I guess some of the info depends on your module as well.

Anyways when you have processed the payment you should return TRUE which will make the simple payment module mark that payment as being processed. I imagine that there is an interface that will allow you to see if a payment hasn't been processed, which would happen if an error occurred while processing.