Digital SLR (DSLR) stands for digital "Single-Lens Reflex" camera. A digital SLR camera differs from point-and-shoot cameras in that the light passes through the lens, bounces off of a mechanical mirror system, and to the viewfinder... or these days, with almost all DSLR cameras utilizing an LCD screen to compose the shot, to a sensor that displays the image to the LCD in real time. When the shutter is pressed, the mirror swings up and the focused light hits an image sensor and captures it, encodes it, and sends it to a memory card in the selected format.
In the last few years, SLR digital cameras have been improved to not only capture still images, but high-def motion video as well. The first two DSLR models to incorporate video capture were the Nikon D90 and Canon EOS (5D) Mark II, but now many different camera brands and models allow the capture of hours of video on a single memory card.
An excellent way to find the best DSLR for your needs is to read digital SLR reviews from knowledgeable photographers or people that have already purchased and used the cameras you are considering. For the best price, look online for digital SLR deals; for example, DSLR packages are available that bundle the camera body, two lenses, a camera case and other camera accessories together for one discounted price.