SLR stands for Single Lens Reflex. All it basically means is you look through the lens to compose the shot. The viewfinder is actually showing you the world THROUGH the lens. As opposed to "point and shoot" where the view finder usually just looks straight through the body of the camera.
SLR also means you can change the lenses. Depending on what you want to shoot different focal lengths and aperature openings are required to get good, consistent shots. By buying different lenses you can match the lens with the shot to get a good picture.
SLRs are traditionally film based ... only recently have the big camera companies delved into the the digital SLR realm. The only difference between a digital SLR and a film SLR is price (the basics of the lens theory remains the same) and the medium on which the picture is burned (film or a CCD).
Point and shoot cameras come with one, fixed lens. Meaning it's a camera of averages - it will (or may) do an "average" job on every picture. You may luck out and find light and distances that work great for that particular lens but that really limits what you can shoot, well.
SLRs allow you to swap out the lens when you need to. And you usually find more advanced features (plus the ability to set everything manually) things like aperature (f-stops), shutter speed, film speed, depth-of-field, etc. You can't mess with these things on a point and shoot because the lens is fixed/and or it's a "lower-priced" camera.
There is a learning curve to a full-fledged SLR but once you get the basics you can really start compsoing some imaginative/interesting shots. Combine that with learning how to develop your own pictures (and film) and the potential for the quality of not only composition but development is un-ending.
To give you an idea... this is the actual camera I just bought. A Canon A-1.
Notice how there is no lens? If that cap on the front is removed it would look like this:
See that mirror in there? When the lens is attached, the lens focuses the image on that mirror which in turn bounces it up and through the viewfinder. When you release the shutter (take the picture) that mirror flips up and allows the focused light to hit the, now, exposed film in the back of the camera.
And this is what it looks like with a lens on the body and what lenses look like off-camera:
The A-1 is actually pretty advanced and is the forerunner of all the modern Canon EOS/Rebel AF SLRs. The A-1 does everything the new ones do but it doesn't have auto focus (AF) which I don't really need anyway.
And it's built like a friggin tank (brass body).