CVT -- continuously variable transmission. Instead of several steps of gears, the CVT keeps the engine running at optimum speed no matter what the road speed is. Because the engine is runs at optimum speed, the CVT gives you considerable fuel mileage. You will save enough gas money to pay for a belt replacement.
My experience with a CVT is on my Vespa 150, motor-scooter. Car (and motorcycle) guys don't like CVT because they cannot know what speed they are doing. Old school, geared, you get up to speed and the RPMs stay steady. With a CVT, the engine stays at a steady RPM, while the vehicle continues accelerating. REALLY WEIRD.
With a scooter, which is what people know about, the CVT has a rubber band, which needs to be replaced every 10,000 miles. Car CVTs have steel belts, and with regular servicing the belt will run will over 100,000 miles and some people are got over 200,000 miles.
Bottom line? Depends on who you listen to. I am a driver, not a gear-head. I don't car about the oh-wows, all I care is "does it work?" I have a scoot with a CVT. CVTs work, save gas, and I would definitely get a car or van with a CVT.