Lens and Focal Length
A camera lens collects the available light and focuses it on the sensor. The important difference between the lens of a digital camera and the lens of a 35 mm camera is the focal length. The focal length is the distance between the lens and the surface of the sensor. The surface of a film sensor is much larger than the surface of a CCD sensor, in fact, a typical 1.3 megapixel digital sensor is approximately one-sixth of the linear dimensions of film. In order to project the image onto a smaller sensor, it is necessary to shorten the focal length by the same proportion. This is why digital cameras and their zooms can be so much smaller than film cameras.
Focal length is also the critical information in determining how much magnification you get when you look through your camera. In 35 mm cameras, a 50 mm lens gives a natural view of the subject. As you increase the focal length, you get greater magnification and objects appear to get closer. As you decrease the focal length, things appear to get further away, but you can capture a wider field of view in the camera.
Since, many photographers that use film-based cameras are familiar with the focal lengths that project an image onto 35 mm film, digital cameras advertise their focal lengths with "35 mm equivalents." This is extremely helpful information to have. In the chart below, you can compare the actual focal lengths of a typical 1.3-megapixel camera and its equivalent in a 35 mm camera.
Focal Length 35 mm Equivalent View Typical Uses
5.4 mm 35 mm Things look smaller and farther away. Wide-angle shots, landscapes, large buildings, groups of people
7.7 mm 50 mm Things look about the same distance as what your eye sees. "Normal" shots of people and objects
16.2 mm 105 mm Things are magnified and appear closer. Telephoto shots, close-ups

Optical Zoom vs. Digital Zoom
In general terms, a zoom lens is any lens that has an adjustable focal length. Zoom doesn't always mean a close up. As you can see in the chart above, the "normal" view of the world for this particular camera is 7.7 mm. You can zoom out for a wide-angle view of the world, or you can zoom in for a closer view of the world. Digital cameras may have an optical zoom, a digital zoom, or both.
An optical zoom actually changes the focal length of your lens. As a result, the image is magnified by the lens (sometimes called the optics, hence optical zoom). With greater magnification, the light is spread across the entire CCD sensor and all of the pixels can be used. You can think of an optical zoom as a true zoom that will improve the quality of your pictures.
A digital zoom is a computer trick that magnifies a portion of the information that hits the sensor. Let's say that you are shooting a picture with a 2X digital zoom. The camera will use half of the pixels at the center of the CCD sensor and ignore all the other pixels. Then it will use interpolation techniques to add detail to the photo. Although it may look like you are shooting a picture with twice the magnification, you can get the same results by shooting the photo without a zoom and blowing up the picture using your computer software.