I have a Jazz as a second car and I gotta say that despite being fairly ugly, its the most practical thing I have ever seen. Its got 4 doors and can swallow a huge amount of stuff and carry 4 people with plenty of room, (which is unlike the Porsche Boxter I am buying to replace my other car). The fuel economy is amazing, especially with the CVT auto. In fact, this transmission is so efficient, its actually faster and uses less fuel than the manual Jazz.
To answer the question at the start of this thread, a CVT is a continuously variable transmission. It theroretically has an infinite amount of gear ratios which allow the box to select the optimum gear ratio to suit and thus make the most out of the engines power and maximise fuel economy. The Jazz CVT, at least on the VTI and VTI-S models also has 7 predefined ratios or gears, controlled by steering wheel buttons, if you want to have a little fun shifting yourself. Grade logic is a feature that is appearing on many automatic gearboxes and is a program within the electronic "brain" of the gearbox. It senses the degree of incline you are on and adjusts the gearboxes shift points to ensure that it is in the correct gear for the conditions. Older auto gearboxes often caused the engine to labour in too high a gear going up a hill, needing you to kickdown or manually shift down, or hunt between gears (constantly shifting up and down) or go in too high a gear going down a hill.