Payment Schedule contains the information needed to drive the creation of payments where they need to recur automatically. Payment schedules have a lookup relationship with Authorisation.
Their only function is to create Payment records, linked to Authorisations (Saved Payment methods) on a fixed schedule so that these payments can be collected automatically.
Most of our customers use their own objects (such as invoices or orders) to drive the automatic creation of payment records rather than using payment schedules.