Battery pack size, or for that matter gasoline tank size, is the primary determiner of driving range. It's a simple equation: Divide the energy stored on the vehicle by the energy consumption per mile, and you have the driving range:
range = energy stored / energy consumed per mile
In an electric car the quantity of stored energy is measured in kiloWatt-hours. One car might have a 24 kiloWatt-hour pack, and another have an 85 kiloWatt-hour pack, or well over 3 times the amount of energy. Assuming the two cars consume energy at the same rate, the second car will have 3.5 times the driving range.
Here's two concrete ways to correlate energy storage, energy consumption, and range.
range = gallons gasoline / gallons consumed per mile range = kiloWatt-hours / kWh consumed per mile
As we see in the next sections, this is overly simplistic. For example, that 85 kWh car weighs a lot more than the 24 kWh car, meaning a higher energy consumption per mile simply because of the weight. Therefore it doesn't get 3.5x the range of the 24 kWh car, but more like 3.1x (85 kWh gives 265 miles range, 24 kWh gives 84 miles range).
Even so, battery pack size is a great first order estimate of range. For example, for several months before GM released details of the Chevy Bolt we knew it would have a 200 mile (or so) range. Making the assumption GM meant the EPA range would be 200 miles, that meant the car would likely have a 60 kiloWatt-hour battery pack. How did we derive this guess? Simple, the 60 kiloWatt-hour Tesla Model S had a 208 mile EPA range. It's a rough extrapolation that 60 kWh gives about 200 miles range. But what really counts is the officially sanctioned EPA estimate, not the number tossed around by the automakers marketing department.