Car dies when I have headlights or heater on

My car turned off while I was coming to a stop the other day, I had just turned my headlights on it jerked and shut off. I quickly shut everything off and then restarted it and it turned on I drove home and parked it. The next day I was driving and turned the heater on and it jerked and I quickly turned the heater off. The airbag light flashed and it felt like it was going to die but did not. Today I was coming to another stop and it died again I had headlights on, I got out and locked the car to run into store and the car would not lock using the automatic lock button it was like my battery was dead. When I came back out it would not start, I waited a few minutes and it started. Does anyone have any idea what might be causing this? Someone told me alternator.