The ending of Planet of the Apes 2001 shows Leo returning to a changed Earth where apes are in charge, with the Lincoln Memorial now honoring Thade.
Leo flies away from the ape planet in Pericles' pod after the fighting stops. He lands in Washington, D.C., but ape police surround the scene, and the Lincoln Memorial now shows Thade. The film stops on that image, which tells the audience that apes rule the Earth he has come back to.
How did it happen? In my reading, the film points to a cause and effect loop that it never fully spells out. Leo reached the ape planet through the storm, found that its forbidden temple Calima was his own station, the Oberon, and then returned through the same storm. Because time had carried him far into the future, his trip appears to have altered the world he came from. This is an interpretation, since the film gives no explicit mechanism.
It could be argued that this is the film's central difference from 1968, directed by Franklin J. Schaffner. That film lands its twist on what has already happened, whereas Burton's version lands its twist on what Leo may have caused, and leaves the viewer with an open question rather than an explanation. Paradoxically, the Thade statue is a quieter shock than a grand reveal, because it asks for one second of recognition and then ends.
For how the three runs of films relate, see planet of the apes original vs reboot.