WHY DSLR ?
DSLRs uses a Mirror, called Penta Mirror inside it to either redirect light coming from lens to viewfinder (what is Viewfinder, explained here) or let the light travel all the way to digital image sensor directly, skipping mirror.
DSLR cameras are just the successor of SLR cameras with Digital Image sensor. It uses the same mirror mechanism to take pictures.
Below picture depicts working mechanism of SLR and Mirrorless cameras:
There are various parts of DSLR camera like lens, reflex mirror, shutter, image sensor, pentaprism and many more. I have tried to list out all these parts here (DSLR Parts).
In DSLR light travels from lens opening and reaches the mirror (Penta Mirror) which in turn hits another mirror with specific angle, and the resulting image can be seen through viewfinder. The viewfinders on DSLRs are large enough to see everything through it very precisely, even if you are focusing @500mm distant object with telephoto lens.
Penta-Mirror is quite helpful in tracking of moving subjects and predictive/continuous autofocus. It helps you to see exactly what the camera “seeing” through viewfinder i.e WHAT YOU SEE IS WHAT YOU GET, it helps you tremendously to compose image and adjust/change you focus on subject.
You can also compose the shot using viewfinder without turning your camera ON while this is not possible with Point n Shoot cameras. So that small mirror saves lots of battery too 🙂
Now when we half press the shutter, using that mirror DSLR locks the focus. And once you press the shutter further, mirror flips up and allows light to directly reach the sensor through lens. Sensor captures all the details and displays the final result on LCD.
WHY DSLR :
Better Picture Quality :
No matter how amazing technology gets, there are some fundamental limitations that will more or less always be in the way of point n shoot and smartphones camera. Larger sensors are, in general, better sensors. They can gather more light and offer more depth of field control and with that large sensor you can get images that are practically impossible with a phone.