The Mark Paid button allows you to mark multiple invoices "Paid" at one time. On the Active Invoices page, just check the box next to the invoices you want to mark "Paid".
Then, click the Mark Paid button on the upper right-hand side of the table. 
In the popup box, you will see a field called, "Partial Payments Already Applied". This shows all partial payments you have already received for any of the invoices you selected in the first step. The "Total Amount Due" is the remaining balance for all of those invoices (once the partial payments have been subtracted). 
Finally, you may choose a payment method from the dropdown box and fill in any payment information needed. For example: If you're using a check for the payment here, you may type in the check number for your reference. 
As always, don't hesitate to reach out with any questions you may have.