Unless a battery is made using superconductors, which hasn't happened yet, at least in commercial batteries, there is a resistance to the materials that conduct the electricity inside the battery, usually only a small fraction of an ohm. For example, on the Duracell Ultra AA (1.5V) battery's datasheet, it says that the internal resistance is approximately 81 milliohms. So the battery itself, because it is not perfectly conductive, provides resistance to the circuit. If you do the math, 1.552V / 81milliohms = 19.16 Amps, the theoretical maximum current output of the Duracell Ultra AA battery. Multiplied by 1.552V, that gives you 29.74 Watts, the maximum power output of the battery.
Of course, different batteries have different internal resistances, but all commercial batteries have an internal resistance which limits the current and power output, preventing a single AA battery from outputting 1500 Watts. If you want to calculate the actual maximum power output of your battery, look up the battery's datasheet, which lists technical information about the battery, and is sure to have the internal resistance listed, though possibly not by that name.