Plants generally capture water through their roots which typically spread evenly in all directions, water travels down through the soil until it hits a ledge then travels along its path (called percolation.) That means a rough measure of the amount of water is plenty to guage requirements for shallow rooted plants, like most food crops. An acre is a measure of area and a foot is a measure of length, combined those give the 3 dimensions to make volume. Water is sold by volume, and for agricultural purposes that is the measure it is sold by to farms (typically.)

One acre of land covered with water one foot deep. One step short of just calculating total volume. Much simpler to work with for the farmers.