When you click on "Settle All Balances", this will make the following window pop open.
Here you can define the minimum payment per affiliate (if you wish to do so). You can hover over the affiliate bubbles to see the amounts payable per affiliate.
To generate the payment file, simply click on "Settle All Balances". This will immediately download the payment file and move all of the "settled" payments to the "Past Payments" section.
Keep in mind that payments are not automated - to officially pay out your affiliates, you'd still need to upload the payment file to a specialized service such as PayPal Bulk Payment.
Note: If you're using the old Payouts page, this article explains how you'd handle payouts using "Prepare Payout Lines".