People have interpreted those eyes in all sorts of ways, but I believe they resemble the eyes of God and/or judgment. Within the description of T.J. Eckleburg, Nick notices a lack of facial features, which supports that idea, because no one can put a real face on God or judgment. It's to big for us to recognize and comprehend. The giant eyes watch over the dirtiest, poorest setting in the book, the Valley of Ashes, constantly watching the corrupted, hypocritical characters pass through without a care or thought for the people living in the Valley, a not so subtle sign of their selfishness. Tom only stops at Wilson's garage for Myrtle, and guess who's peeping through the window. Those eyes represent an observation of lies and adultery as well as the most violent scene of the book. I also think it's interesting that T.J. Eckleburg seems to serve the purpose of a completely objective point of view: no facial features or dialogue, just large, watchful eyes, which contrast Nick's smaller stature almost as a lesser person than T.J., because Carraway's point of view is a subjective and possibly unreliable point of view. Although Fitzgerald never directly discusses the death of the American Dream, as Nick and company attempt to live out their own personal American dreams, Eckleburg's eyes watch the destruction of them all.