Basically, Delivery Status Notifications (DSNs) define a special MIME type to report message status information. The types of information that are transmitted are successful delivery, delayed delivery, or failure, with possibly additional diagnostic information. A DSN is not able to report if a user has actually looked at a message, or any other status beyond "it was placed in their mailbox".
Message Delivery Notifications (MDNs) build on the DSN framework to report the final disposition (seen, discarded, etc) once it has been placed in a user's mailbox. There are some caveats here:
EXMH is able to display both DSNs and MDNs without further configuration. Some additional configuration is required to make full use of the support.
DSN options are located on the 'Preferences - Simple Editor' panel, and are also settable on a per-message basis via the 'DSN...' menu in Sedit. Note that for DSN support to work, you must have a version of MH that supports it (which may require some patching. A patch for nmh 1.0.4 is available in the Exmh distribution in misc/README.dsn-nmh
The EXMH MDN support is able to display a MDN without further configuration. However, to ask for a MDN on a given message, you need to select 'Ask for Receipt' in the Sedit 'More...' menu. In addition, you must put the address to send the MDN to in the 'Preferences - MIME' panel, in the 'Disposition Notification To:' field. This should probably be set to the same address as your From: field, unless you've read RFC2298 and fully understand the implications.
The 'Send MDNs' button in the 'Preferences - MIME' panel controls when to send an MDN. By default, MDNs are not sent. A reasonable value is 'Auto/Ask', which will automatically send an MDN unless a condition is detected prompting a check with the user (such as an MDN directed to a mailing list, or not back to the message sender, etc).
DSNs and MDNs are defined in the following IETF RFCs: