I have a Sony CyberShot camera and I don't know why they use a lens in the camera. What is a Carl Zeiss lens?
A lens is needed to focus light on imaging sensor. For example, here's an image taken without lens attached to camera:
For comparison, same scene taken with a lens attached:
Carl Zeiss is a German manufacturer well known for carefully designed good quality optics; see also what makes a Carl Zeiss lens so special in a smartphone (the reasons are similar for a pocket camera).
A Carl Ziess lens refers to the name of the lens designer and manufacturer. In the days of 35mm film cameras these lenses were considered to be almost the best available. Cameras I had back then with a Carl Ziess lens certainly took great shots. Today I suspect these lenses rely on past reputation rather than being particularly superior to other top lenses.