What's the difference between optical zoom and digital zoom?

It's important to understand this difference, as you could end up mighty disappointed with the results if you get one rather than the other. Optical zoom is similar to what you'll find in a regular 35mm camera: When you push the button to zoom in or out, physical lens elements move inside the camera, to achieve the desired effect.
Digital zoom, on the other hand, has no moving parts. Using the "electronic brain" within the camera instead, the camera takes a look at what it's "looking at", and digitally zooms in, usually two or three times closer.
The problem with digital zoom is that you lose quality when you do this -- your images will tend to be more "pixelated" than the same image taken with an optical zoom camera. This is due to the "interpolation" the camera uses, which is a nice way of saying that it makes a guess about how the picture should look while zoomed in. Having optical AND digital zoom on a camera isn't bad, but I'd try to avoid cameras with only digital zoom, myself.