A pull payment is one of the two directions described in the entry on push vs pull payments: the party being paid starts the transaction and draws the money out of the payer's account. The payer does not send anything at the moment of payment. Instead the payer has given permission in advance, and the payee, through its bank or processor, presents a claim against the account.
Card purchases are the most familiar pull payment, because the merchant submits the charge and the issuer pays it. A direct debit, an ACH debit and a paper check work the same way. Each depends on an authorization, such as a signed mandate or stored card details, that lets the payee collect a fixed or variable amount.
Because the payer's bank only learns of the claim when it arrives, a pull payment can fail for lack of funds or be disputed afterwards as unauthorized. That is why pull systems have return and chargeback rights, and why collection is not final until the return window has passed. The main entry compares these risks with those of push payments.