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Besides having a complete list of transactions of the debtor or creditor, the Payment History enables you to find information regarding invoices and payments (or receipts).
Assuming you issued a credit note for a customer and contra part of it with an invoice. This "information", which is the credit note, the invoice with the contra and outstanding amount, shows in the Payment History.
The Payment History provides an overview and traceability of what and how much has been paid/contra.