What does it mean when car starter makes buzzing noise?

It's typically either a discharged battery or a poor battery connection. Batteries are only an electrical storage device. If the alternator isn't keeping the battery adequately charged you could have the problem you describe. But rather than running right out and replacing the battery, first charge it and see if it will hold a charge overnight. Sometimes, if something is left on inside the car it will run the battery down sufficiently to cause what you describe. Other times it's the alternator, dirty battery terminal or even a worn out battery, but you can't know until you test these components.