A debit note increases what a customer owes on an invoice you have already sent. Use it when the invoice charged too little: a wrong rate, extra quantity, or tax left out. Enter what is being added and the total debit adds up.
A credit note lowers what the customer owes; a debit note raises it. Both point back to the original invoice, which stays as it was.
In Indian trade, buyers also send debit notes to suppliers when they return goods, as a claim against the supplier. Under GST, though, the document that adjusts tax for a return is the supplier's credit note.