Why series arrangement of batteries brighter than parallel arrangement of batteries?

Connecting batteries in series increases available voltage. Connecting them in parallel increases available current. Ohm's law states that when resistance is constant (and a light bulb is a constant resistance, to a point), the current flowing through will be directly proportional to the voltage. And when the voltage doesn't change, the only way to change the flowing current is to lower the resistance - as in, put in a smaller light bulb.