West Egg and East Egg are symbols for the differences in background, attitudes, and actions between Tom and Daisy Buchanan (residents of East Egg) and Nick and Gatsby (residents of West Egg); in a larger sense, between those who lived in the corrupt, money-hungry East and those with the innocence and honesty of the West. In terms of the search for the American Dream, the residents of East Egg thought they had achieved that end because they weren't aware of the emptiness of their lives. Those who lived in West Egg were still searching and hoping to find their dream.
The valley of ashes is the great divide between the two, the physical, moral and emotional symbol of the contrast between the vibrant life on either side. In the valley live the people who have no hope of achieving the dream; through the valley travel those still struggling to attain it and those who don't realize the futility of their supposedly fulfilled lives.