What does it mean if an AA battery has 1.5V written on the side of it?

It means that the potential difference between the metal can and the little button on top of the battery is about 1.5 volts.

That's strictly the result of the chemicals in the battery, and has nothing to do with its size. If a battery as big as a house has the same chemistry inside that the AA has, the big one will also have 1.5 volts between its terminals. (But it'll run your flashlight much longer than the AA will, before it runs down.)

1.5V stands for the voltage of the battery.