There are two types of digital zoom.
The first, often called smart zoom, uses a smaller part of the sensor to make an image of smaller pixel dimensions but with more of the subject in. Often you first have to pick a smaller image size to access it. This is exactly the same as taking a larger image and cropping it on the computer which is fine if you have a computer, I know folk with digital cameras that just take the card into Boots and get printouts. One advantage of doing it on camera rather than in computer is that the image will be focused and exposed for the zoomed in area rather than the total zoomed out area.
The second sort of digital zoom is where the centre of the sensor is used but the image is increased in size back up to the original pixel dimensions. This increase is done by interpolating, guessing!, the extra pixels. It works OK for a few % but after that it looks awful. It is mainly used in video cameras, where the final pixel dimensions are fixed, but can be seen in phone cameras and some cheaper digital cameras.
I can see the point of the first type if you don't like playing about with your pictures on a computer. The second type is hard to justify but for a lot of folk the content is all that matters, they would rather have a bigger but worse image of whatever than a smaller but better one.
If you don't like it you can turn it off.
