What is the debit note invoice for?

Do you mean the difference between a debit note and an invoice?

Debit Notes are transactions signifying a payment that your customer owes you, just like Invoices. In fact structurally they are very much like Invoices. Though they have a different meaning. Invoices always depict Sales or Service rendered , while Debit Notes on the other hand are used for deducting money from your Customer's Account without a sale being made.

Debit Notes are always raised for doing adjustments in the Accounts and is not for invocing a sale to Customer. Invoices are always raised against the sale.

A debit note is issued to a customer for sales returns.

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debt note transaction in A/P module : decrease vendor account 

debt note transaction in A/R module : increase customer account