When you drive through a level you'll noticed the red and white gates clicking up as you drive past. Those are Save Gates.
When you die, you have an option to spend a Power Token to activate the last Save Gate you passed. When a save gate is activated, you can restart from that Save Gate instead of starting all the way back at the beginning of the level.
Note that if you quit the level and exit out completely, your Save Gates for that level will be reset.