Ability Range determines the effective distance and cast range of hero abilities. It is measured in a distance of meters, and stat gains are measured in percentages.
For example, Shiv's Slice and Dice ability has a dash range of 12 meters. Purchasing Mystic Reach improves this by 18%, making the new effective dash range of the ability 14.1 meters.
Stacking sources of ability range increases is an additive effect. For example, having both Improved Reach (25%) and Divine Barrier (8%) will provide a 33% ability range boost.