Delivery URL (DLRURL) is basically the URL where you can get the delivery reports if requested via API. To request such delivery reports, you need to pass "DLRURL" parameter in the API URL.
Trigger URL is the URL where any said event happens and we trigger that specified URL. You need to pass TriggerURL parameter in API for the same. Our application would trigger the incoming request received on application on real time basis on URL configured.
You may follow our API documentation here to know more about such URLs and their parameters.