The context of the quote is "That's my Middle West ... the street lamps and sleigh bells in the frosty dark.... I see now that this has been a story of the West, after all--Tom and Gatsby, Daisy and Jordan and I, were all Westerners, and perhaps we possessed some deficiency in common which made us subtly inadaptable to Eastern life."
Nick realizes that the East is connected with a fast-paced lifestyle, immoral parties, and bad moral values, while the West is associated with a more traditional moral system. Nick then decides to move back to the West. The difference between Nick Carraway and Jay Gatsby arrives when Nick realizes his moral failures and did something to help them.
Sick of the East and its empty values, Nick decides to move back to the Midwest. Just before he leaves, Nick encounters Tom on Fifth Avenue in New York City. Nick muses that, in some ways, this story is a story of the West even though it has taken place entirely on the East Coast. Nick, Jordan, Tom, and Daisy are all from west of the Appalachians, and Nick believes that the reactions of each, himself included, to living the fast-paced, lurid lifestyle of the East has shaped his or her behavior. Nick remembers life in the Midwest, full of snow, trains, and Christmas wreaths, and thinks that the East seems grotesque and distorted by comparison.
Fitzgerald's novel is a contrast of values represented by the West and the East. The West is characterized by virtues, innocence, decency, all qualities we see in Nick and in Jay Gatz. The East, specifically New York, is corrupt and insensitive, words that describe Tom and Daisy. Although Tom and Daisy are originally from the West, living a wealthy life on East Egg has cost them any innocence they might have had and destroyed good qualities; they become "careless people who destroyed other people's lives."
Nick and Gatsby, on the other hand, come East but live in West Egg. Nick is much less affected by the corruption in the East; in fact, he plans to return to the West, to escape the kind of life he's seen. Gatsby, however, is corrupted in his pursuit of Daisy because he's resorted to crime to gain his fortune.
Although the novel is set primarily in the East, all four main characters are midwesterners. When Nick makes the statement you've cited, he reminds us of this fact. Some characters can maintain their goodness, but most cannot when they move to the East. The West is their home.