While optical zoom is the focal length of the lens, the digital zoom, which usually comes with point and shoot cameras, is not an optical function. Digital zoom uses the original picture and interpolates it to create an artificially zoomed image.
Because the digital zoom causes data to be lost, your final image will be of a lower quality. The manual zoom (the “sneaker zoom” - your feet) will always result in a better quality. If you are still not able to get close to a subject, and feel as though digital zoom would help you, recreate the effect later with cropping in a software application.
Digital zoom does not have any benefit. You are actually losing important image data.
Lets say you took the following shot with your digital camera at its maximum zoom of 3x:
You then saw that you could use the digital zoom feature to increase the zoom factor to 10x, and create the following image:
What is happening inside the camera is the 3x zoom photograph is captured and saved internally. The camera then throws away all the information that is not present in the 10x zoom, so your 5 megapixel image essentially now becomes a 1 megapixel image. The camera then interpolates the pixels, and guesses what the rest of the image should look like, and resizes it back to 5 megapixel:
none.