Weight matters for some bridges. It also affects the off road and power ratings.
Speed is self-explanatory, as noted.
As noted above, power is acceleration. Whether it has any other application I don't know. I've always ignored it, to be honest.
All vehicles in CM can turn by rotating in-place. It's an abstraction. The Turning rating is literally how fast they rotate. It's based primarily on the vehicle's real world turn radius.
Off road is bogging resistance, based mainly on nominal ground pressure with some mean maximum pressure ratings for certain vehicles.