DSLR means digital single lens reflex. The difference is that the SLR shows a view to the user via the taking lens and as the camera has interchangeable lenses the subject is shown as it will be in the shot (with accurate focus and without cropping due to zooming).
Among Digital cameras the SLR is larger and is distinguished by a separate optical viewfinder via a pentaprism visible as a lump atop the camera. Many people, including myself prefer an optical viewfinder, because the subject is visible in all conditions, even in bright sunshine that washes out a regular viewing screen.
The term SLR is a little confusing because it dates back to the days when some advanced cameras that used film had a second lens for viewing (example, the Rolleiflex twin lens reflex type). This was not necessarily in proper parallax with the taking lens and depth of focus was not affected by aperture.
The SLR largely replaced both Twin Lens Reflex -- and Rangefinder type cameras (typified by Leicas) -- in no small part because of its quick adoption by Japanese brands like Pentax and Nikon who offered reliable cameras and decent lenses at lower prices than the great German brands.