The Payment Scheduler is a built-in functionality and it works similarly to the Invoice Scheduler, except that it doesn't create invoices, obviously, but creates payments.
While the Payment record is still in Draft status, it's not eligible for Allocations. When its status changes to Posted, the Allocations button becomes available in the top right corner on the Payment record.
When a customer sends in a payment for an invoice, we want to be able to record that in Salesforce and be able to allocate it against the correct invoices. Salesforce Billing tracks and allocates payments using several objects.