Optical zoom is the type of zoom you are accustomed to with your old 35mm camera. Optical zoom is when the lens actually moves in and out and gets you closer to the object. An optical zoom is a real zoom. When you are purchasing a camcorder you will want to look for a camcorder with a high optical zoom.
Digital pictures are made up of tons of tiny dots called pixels. A digital zoom just takes those small pixels and enlarges them. Although it may make your picture appear closer, using a lot of digital zoom in your video can also make your picture look blurry or distorted. If you zoom in all the way using your digital zoom the individual pixels will sometimes be visible as small squares. In most cases you will not want to use a digital zoom over 200x or 300x.
Using a digital zoom can also make any movement the camcorder makes look exaggerated, so it is best to use a tripod when you know you will be using digital zoom. There is a function on your camcorder to turn the digital zoom off many professionals do this in order to preserve the quality of their video.
So how do they come up with that huge number?
Camcorder manufacturers will usually multiply the optical zoom by the digital zoom to get the huge zoom number they put on the box of your camcorder. The larger number is meant to sway you into purchasing their camcorder over a competitors simply because it has a higher zoom. When you're shopping for a camcorder purchase a camcorder with a high optical zoom over one with a large digital zoom. Your video will look much better, and you will overall be getting a much better deal. Read more about camcorders zoom, and find out how much zoom you'll need for different settings in this article: How Much Zoom Do I Need?