it automatically puts it self in the right gear for your driving condition.

This is like a manu-matic or tiptronic or other automatic trans where you can manually shift gears if you want to.  Gas mileage really isn't better but it gives drivers a feeling of more "control."  I find them to be somewhat distracting, I usually run them in automatic mode, the few times I've driven one and put it in "manual automatic" it was just annoying.  There's no clutch, you just move the shifter lever back and forth to go up or down a gear.