Does that mean the camera crops the image? Does the camera magnify the image? Does it change the focal length of the lens? Something else going on?
Well, right off the bat we can eliminate the magnification or focal length questions. The focal length of the lens is a property of the lens and is not changed by what camera body it is attached to. A 50mm lens is a 50mm lens. No special voodoo magic in a camera body is going to change the focal length of the lens. What does change is the field of view of a lens. The lens projects an image circle. Different cameras make use of different angles of view within the projected image. Smaller sensor cameras discard the outer range of the circle. Is that a crop? You have to decide for yourself. I don't think it really matters. But some folks get very religious about this. Look at the figure here and decide for yourself if you want to say the camera is cropping out the outer range of the image circle or if you want to describe it some other way...
In the above example, the full rectagle is what your eye sees. The larger black circle represents the image circle projected by the lens. The blue rectangle represents what a full-frame 35mm size image sensor records. The red rectangle represents what a 1.6 crop-factor camera sees.
I think the entire situation is better comprehended by folks who grew up using a variety of different camera formats--especially a view camera with different size film backs, like my Deardorf 5x7 that also takes a 4x5 back. When you change the camera back from 5x7 to 4x5 without moving the camera or changing the lens you simply get less of the image in the frame. The lens didn't magically get larger. The image didn't magically get larger. The image projected by the lens is still exactly the same. It is just the area of it that is covered by film got smaller.
For those folks who never used a camera before, I don't really think it makes much difference in your taking photos. It does, though, make a difference if you are reading a book or article that assumes you are using a 35mm film (or full frame sensor) camera with lenses designed for those cameras. You have to take into account the crop/conversion factor. When a text says that you need to use a 70mm or greater lens for "normal" perspective in a portrait you have to convert that to say 44mm or greater if you have a 1.6 crop sensor (typical of many Canon dSLR cameras) or 47mm or greater with a 1.5 crop sensor (Nikon). It isn't the lens that distorts, it is the distance between the camera and the subject. But that is the subject for another blog entry.
As for how to describe the small sensor effect, you decide for yourself if you want to call it a crop of the full data or something else. Me? I'll just go out and make more photographs and not worry about it.