Digital zoom - poor man's telelens
Unlike the more advanced digital zooms that work by cropping the central part of the frame and then interpolate it back to the camera's full resolution, the most simple type limits the amount of frame you record by only using the smaller, central portion of the CCD element to represent the same image size as a full screen frame. It reduces the field of view and thereby gives the impression that you are closing in on a subject far away.
If you decide to make prints any larger than say 5” by 7”, chances are the amount of noise present will interfere with image quality. The effect can be compared to graininess in conventional film. For best picture quality ignore this type of zoom since it is no more than a clever marketing trick. It doesn't do anything useful other than throwing away part of your image. The process is irreversible since the image information you have discarded cannot be retrieved.
The thing to remember here is that by doing the same thing in your image-manipulating program you will have much more flexibility. The camera system can only crop the central part of the image while programs such as Photoshop allow you to crop any given area of the frame and will probably give a more satisfying result after interpolation anyway.