It's a transmission that doesn't use fixed ratios - like 1st, 2nd, 3rd, etc.
Basically, the engine can run at any speed, irrespective of the speed of the car, within limits.
It gives the ease of use of automatic transmission, with a smoother ride as there are so sudden shift. By allowing the engine to develop maximum power irrespective of road speed, acceleration is maximized - modern CVTs can out accelerate the same car with manual transmission. Conversely when cruising, the engine speed can drop to just above tick-over when little power is needed - providing fuel economy unmatched by conventional automatic or manual transmissions.
It also removes some of the bad features of conventional autos - for example, there is no sudden 'kickdown', instead power is gradually applied, reducing the risk of losing control in a corner