I am a battery scientist with over 40 years experience.
Most of the answers given refer to the traditional automobile where once started the alternator provides most electrical power for vehicle operation. The battery is only required to deliver sustained power for various vehicle loads when the engine is not running,
There are, however, vehicles that make more demands on batteries in order to improve fuel efficiency and reduce pollution. When these vehicles come to a stop light during normal operation, the engine shuts off, thus saving fuel that is wasted in idling. All the electrical loads in the vehicle are then supplied from the battery rather than the alternator that produces nothing while the engine is off. This can normally occur for different lengths of time depending on traffic conditions, but when the driver removes his foot from the brake or touches the accelerator, the engine restarts almost instantly and the alternator recharges the battery.
Obviously, both the battery and starter must be tailored to this scenario. The battery is normally larger and has features to improve its resistance to cycling and charge acceptance. The starter system must be designed for many more starts and do so quickly so as not be very noticeable by the driver. To keep the battery in condition that will prevent its failure to restart during a stop event, a battery monitoring system (BMS) is added to constantly measure the battery痴 performance and keep it in a satisfactory operating condition. The vehicle will not shut off the engine if the BMS or vehicle computer does not approve because of a weak/discharged battery or if some other safety or comfort system would be compromised. Most manufacturers are implementing a version of this system on their new vehicles because of pressure to comply with fuel and emission standards. It only takes a short time to get used to this system (it has been on hybrid vehicles for a long time). Many people are uncomfortable with this change, because it is different. But it is the future and will soon be the standard.
It used to be that batteries were heavily drained by forgetting to turn some electrical load off, like lights. Now most cars have run down features that turn off any load after a period of time.