SLR (Single Lens Reflex) is a camera which typically uses a mirror and prism system that permits to view exactly the same what will be captured at the end. Photo capturing mechanism is almost the same in old days film SLRs and in modern DSLRs. But DSLR is equipped with a sensor and digital storage device instead of film to store the photograph. Most distinguished difference between a DSLR and a compact camera is the lens. In a compact camera, you can’t change the lens as you want. If your manufacturer says its 24mm-500mm, that’s it! You cannot go beyond that.
But in DSLR you are free to choose the lens as you want. In SLR world, lens should fit for the purpose. If you are taking portrait photographs, 50mm standard lens would fit it mostly. If you are into wildlife photography, you would need a telephoto lens for the job. Normally most of the amateur and mid-ranged DSLRs packed with a standard lens. But most of the vendors would give a chance to change the lens if you want or sell the camera with an additional lens. Therefore you should be extra careful when choosing the DSLR since your lens might not be suitable for your expectations with the camera.
Another main advantage with DSLR is the ability of changing the settings as you want. In all DSLR cameras it should possible to change the shutter speed, aperture and the ISO sensitivity. If you are not familiar with these words, just forget them. At least most of DSLRs have many different pre defined picture modes and processing techniques which you can use to snap a good picture.