Before an e-mail message gets delivered to the intended recipient, it gets passed through a series of servers on the Internet called e-mail routers or hops (think of them as Post Offices). Most of these servers are configured to try to deliver the message for a certain period of time. If the message cannot be delivered for one reason or another within this period, then it will be returned to the sender as a Delivery Failure Report.
If the router knows right away it will never be able to deliver the message because, for example, the e-mail address of the intended recipient is invalid, then a Delivery Failure Report is generated and sent to the sender instantly. However, if the router at the recipient's organization is temporarily out of service, the message will be queued up and sender's router will make multiple attempts to deliver it (usually for four days), until it generates a Delivery Failure Report.