Who is Dr. T. J. Eckleburg? What is his significance?

Dr. T. J. Eckleburg's monocled eyes are painted upon an aged billboard; his eyes look down upon the valley of ashes (created as a dumping ground for the negative spoils of capitalism and industrial expansion) through which the characters drive while traveling to Manhattan from West and East Egg. The eyes are thought to represent the eyes of God looking down upon man, whose moral bankruptcy has left the land below literally and metaphorically barren. Although Fitzgerald never directly asserts that the eyes represent God, to the character George Wilson, they do.
Since the definitive meaning of Dr. T. J. Eckleburg's eyes is always somewhat opaque, it is possible the eyes are related to the idea of subjective meaningfulness, which Nick ponders later in the book. In other words, some things or objects mean something to certain people, but other people may look upon the same object and see it as meaningless.