A callback URL is an address on a merchant's or partner's server that a payment provider calls to report what happened to a payment. It is set in the provider's dashboard or included in each request. When the payment's status changes, the provider sends an HTTP request to that address, a mechanism also called a webhook notification.
The term covers two different things that are easily confused. A server callback, sometimes called a notification URL, is called by the provider's systems and is the authoritative signal that money has moved. A return or redirect URL is where the customer's browser is sent after approving a payment on a bank or wallet page, as in a bank redirect; it should not be trusted alone, because the customer can close the page or alter the address. Callbacks are essential for any asynchronous payment. The endpoint must verify each message's signature and tolerate duplicates sent under a webhook retry policy.