What this feature allows the User to do is confirm that an email was sent to the recipient and should be on the recipient's side somewhere. Perhaps suggesting to them that they should 1) add the sender's email address to their allowed senders list, and 2) check their spam folder for the message.
This feature is similar in concept to what the "Request Read Receipt" feature does. However, that feature requires the receiver's mail client to respond to the request... Many mail clients don't respond to those requests at all, while some require the User to click "ok" to say they want to send a receipt. The net effect of this is that read receipts are often not sent back.
The Delivery Receipt will always, for all messages, be sent back when requested. Failure to receive a delivery confirmation may indicate a problem with the email or service and should be reported to MRSware Support. Keep in mind that email delivery is not always instantaneous either, as some receiving mail servers do purposely delay the receiving of email (as a spam prevention method in most cases).