As opposed to optical zoom - which is a magnification of the image through changing the lens's focal length - the term digital zoom refers to cropping the central part of the frame to make up a new separate image. Some systems will then interpolate the cropped part back to the camera's full resolution, while with others the number of pixels left will still be enough for a quality image.
With today's multi-megapixel cameras you do not always need maximum resolution for optimum results. Cropping a 10-Mp image by applying digital zoom could leave you with a 4 or 5 Mp image, which can easily be output at print sizes of up to A4, without any significant loss of detail. An added advantage will be that, as the camera only meters for the zoomed section, a better exposure for that particular area can be achieved than by metering the full screen image. Also, with plenty of megapixels on offer, digital zoom can achieve a much larger zoom factor than would be possible with the optical lens system alone, whereas file sizes will be smaller since you only need to save part of the full screen image.
Although the effect of digital zoom can also be achieved in most image manipulation programs, it can be a useful tool as it will save on post processing time later.