VAC = Volts AC
AC = Alternating Current

Batteries produce DC, or direct current. This is a voltage that does not vary in a short period of time, and can be thought of as a steady stream of electricity. (we won't discuss the difference between current and voltage here)

Alternating current, however, not only varies with time, but changes polarity with time. Household current (in nearly every country) forms a sine wave with a period of either 60Hz (cycles per second) or 50Hz.

Edison (Thomas Alva) proposed to the public that DC was the way to go to power houses, and demonstrated this by using AC to electrocute dogs, horses, and other assorted living things. Westinghouse, however, supported AC, and chose not to kill anything, though DC is just as dangerous for all living things, and it could be argued that it is more dangerous. Whether AC won because of its merits, or because it was easier to make an AC generator than a DC generator/rectifier/etc, and passive AC transformers are cheaper than active DC transformers, we can only opine.

Also see Why my sister couldn't let go of the electric dog fence