Paying off an invoice from the invoice overview page, marks it as paid/partially paid. At the same time, a payment received entry is automatically created. If the registered amount is higher than the value of the invoice, it will be recognized as amount in excess, which can be used in payment of future invoices issued to the client.
Furthermore, when a payment is added in the payments received menu without being associated with any invoices, it will appear as amount in excess. You will be able to use the amount by clicking +Add payment on the bottom of invoices (related to the contact) or by editing the payment entry. Until you do so, however, the "Payment for" column on the list of payments appears blank, as shown below:
Note: This is also how payments received will appear when you disassociate one from a document (Invoice, invoice of services rendered c.) This could happen in cases where a payment has been removed from an invoice in order to proceed with editing or a cancellation. In this case, clicking +Add new payment-> Use amount in excess will pay off the saved invoice, avoiding any duplicates.