It is with batteries that the electrons are stored that make the vehicle move. Roughly speaking, the number of electrons you can store in the vehicle determines how far it will go. The angst of batteries in electric vehicles is the speed and range characteristics you can get in the vehicle using the battery technology available. The common battery technology, lead-acid batteries, have been in use for nearly 200 years and have changed relatively little in that time. By contrast think of the changes and improvements the internal combustion engine has seen in that time.
Power density is the core measure controlling the speed and range you can get with a given vehicle. Power density controls the quantity of electricity you can store within a given space, and is measured two ways: (For more about these units see http://visforvoltage.org/book/ev-batteries/13232)
Energy Density and Power Density are two ways to measure the speed and range you can get with a given vehicle. Each vehicle has a maximum weight it can carry, and a maximum volume or size it can carry. Together those form a budget into which you fit the people, cargo, drive train, electronics, and battery pack.