Digital camcorders have both an optical and digital zoom. In digital video, your picture is made up of thousands of tiny squares called pixels. While the optical zoom on your camcorder will use your camcorders lens to get closer to the picture, the digital zoom on your camcorder just takes those individual pixels and makes them larger to give you the impression you're getting closer to an object. If you use a lot of digital zoom then your video will start to get pixelated, which means you can see the individual squares (or pixels) in your video. You'll especially start to notice individual pixels when you're trying to zoom in on something very detailed like a person, or words on a sign.
Read more about Optical and Digital zoom in: Optical vs. Digital Zoom.
In general, you want to try to find a camcorder with a high optical zoom, and use that whenever possible. There are some situations however, where the digital zoom may come in handy. Here are a few examples of situations where you might use your camcorders zoom, and what amount of zoom you'll need to get the job done.
Close-ups of a child's face at a birthday party
For close-ups of people you're in the same room with you shouldn't need to use more than a 5x or 10x zoom.
An individual soccer player during a game
For soccer games you are typically recording video from the stands. For your typical soccer field you will probably need at least a 25x zoom. Try to not use your digital zoom at all. Soccer games tend to move quickly, and players uniforms have a good amount of detail in them; digital zoom will make the players hard to recognize and even harder to watch.
Performers on a stage from the back of an auditorium
This is another situation where you want to not use your digital zoom. A zoom of 25x or more should be all you need for your average high school auditorium. Try out your zoom before the show, and if you're far away ask someone if you can record from up from on either side of the stage (so you're not in anyone's way). You're video will look much better.
A rainbow off in the distance
Something like a rainbow is one of the few instances where your digital zoom will come in handy. Since rainbows are typically large, with not a lot of detail (except for colors) you can use your digital zoom (even up to 1000x) to shoot one far away. When you use a lot of digital zoom your hand motions will be magnified, possibly to a point you can't stay focused on the rainbow. If you run into this problem use a tripod, or any other stable surface you have available such as the top of your car to keep your camcorder stable.