First lets make the distiction between 'optical zoom' and digital zoom' Digital zoom is enlarging a portion of the image in the camera, thus 'simulating' optical zoom. In my opinion, digital zoom is almost always best avoided and I always disable the digital zoom function in my camera.
Optical zoom (a zoom lens) is basically a telescope attached to the front of your camera. And what a great invention it is. A zoom lens allows you to apprently get a lot closer to distant detail. A real must for wildlife photography, you can use the zoom to 'get up close and personal' to animals that wouldn't let you get anywhere near them for real.
An effect of the zoom lens you need to be aware of is that when you shoot long, the depth of the resulting photo appears diminished.
Zoom is useful in so many situations. The obvious ones such as animal photography are clear to everyone, but zoom also has its place in fashion portraits, landscapes and even macro.