What do automobile makers mean when they say their cars are more powerful than their competitors' cars

High rate of acceleration.

Explanation:

For an automobile power is meant by the power of engine i.e. the amount of energy the engine can deliver in a unit time to the powered-axle of an automobile. Practically it tells about the high throttle of the engine or the acceleration of the engine. This tells that in a very less time duration the car can attain high speed, also called pickup in the fancy term.