I always explain the first three chapters of The Great Gatsby as the exposition to the novel, as it introduces all of the significant characters, the significant locations, and the beginnings of conflict.
In chapter one we are introduced to the narrator, Nick Carraway, and his purpose for leaving the Middle West and heading to New York, which is more about filling a void left by the war than any real desire to become a bondsman. We are also introduced to Tom and Daisy Buchanan and the elitism and lifestyle of East Egg (occupied by "old money" who find the "new money" of the 1920s threatening and contemptuous in their overt display of wealth). This distinction is also made in the architectural references of the chapter (Tom and Daisy's classic Georgian colonial representing understated wealth and prestige vs. Gatsby's palatial Italian villa monstrosity representing flamboyance and excess). Conflict in Daisy and Tom's marriage is also introduced through the phone call from Tom's mistress.
In chapter 2, we are introduced to the setting of Manhattan (the fantasy land for the rich--a false reality) and the Valley of Ashes (the dumping ground/wasteland of the wealthy). We are also introduced to Myrtle Wilson, Tom's mistress. Through her we see the absurd mimickings of the wealthy and how the wealthy are perceived by the lower classes (look at the things Myrtle does when they go to New York--i.e. buys the dog, insists on throwing a party, changes into an overly formal dress and discounts its value to her when she is complemented on it). Chapter two also furthers the conflict in Tom's marriage as well as highlights his elitist behavior (he has no intention of leaving Daisy for Myrtle, and openly abuses Myrtle, whereas he resents Daisy saying in chapter one that he is a brute because he bruises her finger).
In chapter three, we are introduced to the title character, Jay Gatsby, as well as the fourth significant setting West Egg, representing "New Money" and its excesses. Nick is invited to the party at Gatsby's house which epitomizes excess, as well as the relaxed rules of the wealthy (i.e. the free-flowing liquor during Prohibition). We also see the elitist attitude of the "old money," who don't mind partaking in the events, but who refuse to associate with the "new money" and even criticize their host through their gossip. It also establishes the shallow relationships between characters and provides the grounds for Gatsby's near total abandonment later in the novel.
You'll find a fairly detailed discussion of these chapters in the enotes study guide to that great novel starting here: http://www.enotes.com/great-gatsby/30926
In a nutshell, though, in Chapter 1 Nick moves to Long Island to get into the bond business, spends time with his cousin Daisy, and first hears of Gatsby.
In Chapter 2, Tom and Nick go into the city, and Nick learns Tom is having an affair.
In Chapter 3, Nick goes to a party at Gatsby's, sees Jordan (who he knew from before), and meets Gatsby.