A CVT is a continuously variable transmission. They operate by having a steel belt (chain in the case of Audi) that travels under VERY high tension between two variable diameter pullies. Starting out, the "input" pully will start out at minimum diameter, and the "output" pulley will be at maximum diameter. As you accelerate, the input pully wil increase it's diameter, while the output side decreases diameter, keeping tension constant on the belt. The result is a gearless power transmission with no "steps" between ratios. With this arrangement, engine RPM can be constant (say 3,000 rpm for acclerating), while the transmission continuously "reratios" itself throughout the acceleration process. The result of this is manual transmission like fuel economy, with automatic convenience, in a package that is a simpler design that either one.

My Saturn VUE has a CVT in it. I wouln't consider a conventional automatic in another new car. I absolutely love it.

Snowmobiles use a mechanically acutated version of a CVT that has no lubrication at all, and a rubber drive belt - which of course must be replaced. Automotive CVT's are actuated with an electronic hydraulic system.