George Wilson enters a state of grief and perhaps shock after his wife Myrtle is run over by a car in a hit-and-run accident. Just before her death he had learned that "something funny" was going on with Myrtle and had made plans to take her away.
After her death he struggles to remain cogent. Looking up at the billboard with eyes of Dr. T.J. Eckleburg, Wilson becomes confused. He believes that the eyes on the advertisement are the eyes of God.
Now the eyes are most explicitly equated with the eyes of God, the omniscient witness to the tragic incident...(eNotes)
Seeing the eyes on the sign, Wilson says that "God sees everything" and implies that, though he does not know who killed is wife and who she was sleeping with, God knows.
There is a moral code that has been broken. Retribution is inevitable. This is implicit in Wilson's attitude in this episode and serves as a condemnation of the immoral attitudes of the "high class" society, which have led to death, strife, and soon lead to murder.
It is Wilson who carries out this murder after having seen the eyes of Dr. T.J. Eckleburg on the billboard. We may wonder if those eyes inspired Wilson to carry out the retribution that he felt was inevitable. We can say certainly that Wilson believed someone was guilty and that he associated this guilt with God and with a supreme moral transgression.
On the simplest level, however, we can say Wilson's grief and confusion are evident in his reaction to the billboard.