It stand for Single Lens Reflex.
In most (cheaper) cameras the hole you look through is NOT the same as the lens taking the picture. That means you are never taking EXACTLY what you want to take.
With an SLR, when you look through the viewfinder you are looking through the actual lens that takes the picture. So when you take a picture of exactly what you are seeing.
This also means that if you have a wide angle lens, or a long focus lens, you see exaclty what the lens is seeing.
As you take the picture a small mirror "jumps" out the way allowing the light to hit the film (or CCD in a digital camera)
a 35mm SLR is just an SLR camera that takes 35m film, the film that most cameras use (befire most of the world went digital)
Here is a picture showing how it all works.
http://www.yesmag.bc.ca/how_work/slr_camera.gi f