When you have more than one battery in a regulated mod, the load is distributed across them evenly. For example, if we have 3 batteries currently at 4v each in series, we have a series voltage of 12 volts. That is pretty easy to understand. Now, if we are
vaping at 120 watts, we are taking 12v at 10 amps, making 120 watts. Since you have already added the batteries together, you are already factoring in the load distribution. That means each battery would be supplying 10 amps.
Now, if we say we have the same 3 batteries at 4v each, but they are in a parallel configuration, we have 4 volts on the input side. If you are vaping at the same 120 watts, it is going to have to draw 4v at 30 amps to get the 120 watts. When you spread the 30 amps out evenly across the 3 batteries, you end up with each battery supplying 10 amps.
Now lets do the math with a dual battery mod. If you have two batteries in series each putting out 4v for a combined 8v, and you are vaping at 120 watts, you are going to be drawing 8 volts at 15 amps. Since the batteries are not parallel, that means each battery is supplying 15 amps. If they are in parallel, you would have 4v going in. It would need to draw 4v at 30 amps to get to the 120w. Since they are parallel, the load is distributed, and that means each battery is putting out 15 amps.
From there, we can see that having that third battery in a mod reduces the amp loading on the batteries. This will typically lead to slightly longer run times. In addition to the amp loading being reduced, a third battery simply gives you additional capacity. A pair of 3.7v 3000mah batteries has a total capacity of 22.2 watt hours. If you have three 3.7v 3000mah batteries, you have a total capacity of 33.3 watt hours. An easy way to understand watt hours is to relate it to a car. Think of the watts you are using as the amount of gas it takes you to drive 10 miles. Think of the total capacity like your gas tank. If you are using the same amount of fuel, but you suddenly have 50% more fuel in the tank, you can go a lot longer before you have to stop.