When running the car sources it's electricity from the alternator. If you disconect the alternator the car will run on the battery. If you disconnect the battery the car will run on the alternator. Under heavy electrical load the alternator can be taxed to it's limit. At those times some current flows from the battery to make up the differance. If there are no accesories, lights, etc. on the car runs from the alternator. The alternator and battery are in parellel. The reason the alternator charges the battery is because it puts out about 14VDC. The battery fully charged is about 13VDC. If you put a voltmeter across the battery terminals with the car running you should see 13.5 to 14.5VDC. If it is less than that there are several things that could be wrong:
1> Battery
2> An electrical short
3> Faulty alternator