What are 3 symbols from The Great Gatsby and how are they each significant? What do they teach us about society and the characters in the novel?

There are many symbols in The Great Gatsby. I will write about three: the green light, the valley of ashes, and Gatsby's clothes. 

The green light. Gatsby, from his house in West Egg, can look across the Sound and see Daisy's house. He is often seen standing on his lawn at night, looking wistfully toward a green light that burns on Tom and Daisy's dock. Clearly, this provides a focus for his longing for Daisy, who seems so remote from him, yet so sublime, like a star. In Chapter Five, when Gatsby finally gets to meet Daisy again, he tells her, 

"If it wasn't for the mist we could see your home across the bay ... You have always have a green light that burns all night at the end of your dock."

Daisy put her arm through his abruptly, but he seemed absorbed in what he had just said. Possibly it had occurred to him that the colossal significance of that light had now vanished forever.

The significance has vanished forever because now that he has the presence of Daisy herself, his enchanted dream of her is gone. The light, then, could be said to symbolize not just Gatsby's longing for Daisy and her way of life (which Nick calls Gatsby's "incorruptible dream"), but also the transience of that dream, the impossibility that things could actually be as Gatsby imagines.

The valley of ashes. The valley of ashes is Nick's term for an industrial area between West Egg and New York City.   

In one of the links below is an article where the author shows the actual historical location of the valley of ashes, "the vast trash-burning operation in north-central Queens in the exact spot that is now Flushing Meadows-Corona Park." So, this was a historical place that Fitzgerald no doubt passed through. In the second link, the same author points out the similarities between the valley of ashes and the circles of hell in Dante's Inferno. Indeed, Nick's description of the valley sounds hellish.

The valley of ashes is as different as could be from the large, gracious houses of East and West Egg. However, the residents of the Eggs have to pass through this valley every time they go to the city. They cannot ignore it. So, among other things, it symbolizes the vast difference between their lives and those of working-class people.

The inescapability of the valley of ashes hints that it symbolizes something deeper as well. Though the Buchanans would never consider living there, and Gatsby has spent his whole life trying to escape from places like this, nevertheless some of the novel's most important events happen there. This is the home of Tom's mistress, Myrtle Wilson, and her husband George, who runs a garage. It is in the valley of ashes, right in front of the Wilsons' garage, that Daisy runs over Myrtle Wilson while driving drunk. It is from the valley of ashes that George Wilson emerges to confront Tom and kill Gatsby.

In other words, though Tom, Daisy, and Gatsby have tried to insulate themselves from the valley of ashes, they end up having to deal with it, and it even in a sense comes after them. You could say it symbolizes Death, Fate, or perhaps Real Life.

Gatsby's clothes. Gatsby creates the impression of fabulous wealth and decadence with his huge house and massive parties. This extends to his clothes. There is the scene in Chapter Five where Gatsby, manic with joy at finally meeting Daisy again, opens his closet and starts throwing his shirts out onto the bed for her to admire. They are in glowing colors, "shirts with stripes and scrolls and plaids in coral and apple-green and lavender and faint orange."

Daisy cries at this point, saying, "It makes me sad because I've never seen such—such beautiful shirts before." Obviously this is not why she is really crying, but it may be true that Daisy has never seen such gaudily colored shirts. Gatsby is newly rich and probably has wilder taste in shirts than Tom, whose taste is likely to be more restrained. This is also a picture of Gatsby's character. His imagination is full of impossibly beautiful hopes and longings, and he is willing to do anything to make them happen, just as he is the sort of person who buys dozens of shirts every season.

This theme of Gatsby's clothing revealing his class and character is continued in Chapter Seven, the scene of the horrible showdown between Gatsby, Daisy and Tom. Early in the chapter, when Tom has just figured out that Daisy loves Gatsby, someone mentions to Tom that Gatsby is "an Oxford man." Tom sneers, "An Oxford man! Like hell he is. He wears a pink suit." Tom will use this same contempt, within the hour, to separate Daisy from Gatsby.

Gatsby is still wearing the pink suit at the end of that awful evening, when Nick remarks that "I must have felt pretty weird by that time, because I could think of nothing except the luminosity of his pink suit under the moon." At this point, Nick is angry and disgusted with Gatsby. The cheerfulness of the pink suit seems glaringly inappropriate after what has just happened.  t makes Gatsby, with his dream of the ideal, wealthy life with Daisy, seem out of touch and uncaring, though in fact he is neither of these things. It is true in contemporary society, too, that people can feel judged and alienated if someone shows up looking much better dressed, or much more fashionable, than everyone else.