If you buy a non–high-end digital SLR (DSLR) camera, it will probably come with what's known as a "digital" lens. There's no such thing, really: lenses for any kind of camera are analog devices that bend light with glass—or maybe plastic—just as they have been since lenses were invented centuries ago.
What "digital" means in this case is that the lens is designed to be used with the most common type of digital SLR camera, those with crop-frame sensors. Crop sensors are smaller than the traditional 35 mm film dimensions used in more expensive full-frame sensors. So lenses designed for them project smaller circles of light. If you put them on a full-frame camera (that is, if they will even mount), this is what you get:
My AF Nikkor 18-135 mm f/3.5-5.6G digital ("DX") lens has a big black vignette circle around the image when zoomed out to 18 mm and mounted to my full-frame Nikon F4 film SLR. Click the image to see a representation of where a crop-frame sensor would fit in the image circle.
Lenses for traditional non-digital and full-frame SLR cameras also work just great on crop-frame models, but the extra money you pay for their wider image circles goes to waste, because the image around the edges doesn't get captured on the sensor. But I own one crop-frame lens for my crop-frame camera, and several full-frame lenses. Why?
The benefits of buying crop-frame digital lenses are that they're smaller, lighter, and cheaper—and they may offer focal lengths unavailable in their bigger brethren. But the benefits of buying full-frame lenses, conversely, are that they will still work fully if you later upgrade to, or want to borrow or rent, a full-frame camera body; and that they are generally better built because they are aimed at the professional photographers who tend to buy full-frame.