Dogwood berries (Cornus florida) turn red in September as a signal to the birds that the seeds are ripe and ready to be eaten by birds (squirrels eat them too, but they chew up the seeds in the berries). The birds swallow the berries, digest the "meat" off the seeds, and then the softened seeds pass through the bird's digestive system. All of the white woodland dogwoods seen blooming in the spring were planted by birds! :)
People often want to know if berries are edible or poisonous; I do not discuss edibility of plants much on this site due to the danger of misidentification. I do write about poisonous plants. There are good books written on edible plants.