The reason we verticut is to control the thatch buildup in the greens. Too much thatch will lead to increased disease and pest activity, reduce the oxygen supply, and also create shallow roots and localized dry spots.
Benefits include opening the canopy, removing thatch, and standing the blades upright. When the canopy is opened up, more direct sunlight is allowed in to create a healthier plant. Thatch can become an issue in excessive amounts and can make the greens feel spongy. With the blades upright, the greens will roll smoother and, in effect, increase speed and trueness of roll.