In the movie's final scene, Forrest sits on a bench with his son, Forrest Jr., and sees him off on his first day of school. Before parting, they each say that they love the other. And then, we enter some kind of time warp as Forrest Jr. gets on the school bus and introduces himself to the driver in almost the same way Forrest Sr. did as a boy.
Once Forrest Jr. is gone, a feather flies off of Forrest and up into the sky, which mirrors the feather image that starts off the movie. All in all, the scene suggests that the circle of life will keep on going and that in the end, we're all like feathers sometimes, blown around by the events in our lives. As we learn from Forrest and his son, the important thing that we can control is how much we love one another with the time we've got.