The eyes of Dr. Eckleburg are literally eyes on a billboard and figuratively witness to the comings and goings and the deeds of those who pass through the Valley of Ashes.
...the symbolic eyes of Doctor T. J. Eckleburg [watch] over this “solemn dumping ground” as a God-like witness to the...hopelessness that emanates from the place.
While Myrtle and George Wilson, people of modest means, live within sight of this billboard in the modern pseudo-waste land between the suburbs and the city, characters like Gatsby, Tom, Daisy and Nick only pass through this depressed and depressing area.
This region is where Myrtle is killed and where Gatsby's fate is sealed.
The characters in the novel behave badly, acting without any clear moral sense. Though there is little mention of religion in the text, the eyes of Dr. Eckleburg are directly associated with the eyes of God. They stand as the symbolic witness and judge of the events that have taken place, leading to the deaths of two people.
George Wilson draws this comparison after his wife is killed, confusing the eyes on the billboard with the judging eyes of God.
Thus the eyes are a literal representation of commercialism (placed on an advertisement) and a figurative/symbolic representation of a silent force of judgement that finds its place at the end of the novel.
F. Scott Fitzgerald's novel The Great Gatsby is full of symbolism, and the eyes of Dr. T. J. Eckelburg are an important example of this. In the Valley of Ashes, a desolate and ruinous place on the way from West Egg to Manhattan, there is a billboard advertising the services of an oculist (which is what optometrists were called in the 1920s). Nick Carroway describes the billboard as a huge pair of blue eyes wearing yellow glasses and without any other facial features. The condition of the billboard, weathered with age and dirty, suggests that Dr. T. J. Eckelburg is no longer practicing in the Valley of Ashes, but his omniscient eyes watch over the events of the people there. This billboard first appears in chapter two when Tom takes Nick to meet his mistress, Myrtle Wilson, a resident of the Valley of Ashes.
But above the grey land and the spasms of bleak dust which drift endlessly over it, you perceive, after a moment, the eyes of Doctor T. J. Eckleburg. The eyes of Doctor T. J. Eckleburg are blue and gigantic - their retinas are one yard high. They look out of no face but, instead, from a pair of enormous yellow spectacles which pass over a nonexistent nose. Evidently some wild wag of an oculist set them there to fatten his practice in the borough of Queens, and then sank down himself into eternal blindness or forgot them and moved away. But his eyes, dimmed a little by many paintless days under sun and rain, brood on over the solemn dumping ground… I followed [Tom] over a low white-washed railroad fence and we walked back a hundred yards along the road under Doctor Eckleburg's persistent stare . . . "Terrible place, isn't it," said Tom, exchanging a frown with Doctor Eckleburg.
Fitzgerald uses personification here to give human qualities to the billboard when he suggests that it shares a frown with Tom.
The next time readers encounter the eyes is in chapter seven when they foreshadow the tragic events to come.
Over the ashheaps the giant eyes of Doctor T. J. Eckleburg kept their vigil but I perceived, a moment, that other eyes were regarding us with peculiar intensity from less than twenty feet away. In one of the windows over the garage the curtains had been moved aside a little and Myrtle Wilson was peering down at the car.
In this chapter, Myrtle's husband has found out about her affair and is keeping her locked away. Myrtle is staring at the yellow car, thinking it contains Tom who will come to her rescue. Of course, this is how she meets her tragic end, by running out in front of the car.
In chapter eight, readers learn that George interprets the eyes as the eyes of God, watching over his wife's actions in judgment. He proclaims that God—the eyes—watch her, and while she may have been able to fool him, she can't fool God. He says to Michaelis, the coffee shop owner,
"—and I said 'God knows what you've been doing, everything you've been doing. You may fool me but you can't fool God!' "
Standing behind him Michaelis saw with a shock that he was looking at the eyes of Doctor T. J. Eckleburg which had just emerged pale and enormous from the dissolving night.
"God sees everything," repeated Wilson.
"That's an advertisement," Michaelis assured him.
A billboard, metaphoically representing an omniscient being who wathces over the valley of the ashes.