1- Larger sensor
DSLR's have MUCH larger sensors than point and shoot camera. A larger sensor means that the receptor density (the amount of receptors per area) is much lower ... this results in images with less digital noise and a greater dynamic range (better colors). It also typically results in much better low light performance (higher iso with much less noise).
2- Egronomics
Controls on a DSLR are usually in more convient places to reach allowing you to quickly sewitch settings. I tried changing the white balance on my friends sister in laws camera last night and it was a 6 click affair while on my DSLRs it a one click process.
3- Lenses
with a DSLR you have access to different lenses for different situations. when I shoot a wedding, I typically use 2 lenses ... a 24-70 f2.8 for group shots and portraits and a 70-200 f2.8 for portraits and to shoot from a distance without being obtrusive. If I then needed to shoot sports, I could swap that ot for a 400mm f4 or a 200-500 f2.8, if I needed to do macro shots for a jewelry catalogue, I could switch to a nice dedicated macro lens ...
The lenses are also normally far superior in term,s of optics than the built in, does it all lesnes on a point and shoot. also, the point and shoot zoom is only partially optical ... once you pass a certain point the zoom is DIGITAL meaning that it would be like zooming in in photoshop ...
4- Peripherals
Cable releases, flashes, radio triggers ... DSLrs have a whole slew of accessories giving you far more options to work with.
5- MANUAL MODE!
Most point and shoot cameras don;t let YOU decide how to take the shot. The camera makes practically all the decision in terms of exposure, focus, shutter speed, ISO, aperture ... you have limited access to these controls and so you are cut out of like half of what being a photographer means and even if your P&S is actually half decent and give you full manuall access, the controls are not designed for this and it's a pain to make the nedded changes (see ergonomics above).
6- RAW mode.
DSLRs can save ALL the sensor data ... this gives you far more control over the image in post processing.
That should be enough to start.