Gatsby very much wants Nick to help him in his quest to reunite with Daisy so he takes him to lunch in the city. On the drive in, Gatsby knows it is important to dispel some of the rumors Nick would have heard about him at his party. So he offers to tell Nick about his past.
What Gatsby tells is a mix lies and truth. He says he comes from a rich midwestern family, but then undermines that by saying the "midwestern" town he comes from is San Francisco, which is on the west coast. He also says he has hunted big game in the capital cities of Europe, which is impossible, as big game, such as lions and tigers, are not wandering around those cities. Nick has to avoid laughing and thinks:
The very phrases were worn so threadbare that they evoked no image except that of a turbaned "character" leaking sawdust at every pore as he pursued a tiger through the Bois de Boulogne.
In other words, Nick believes that this cliched story comes straight from cheap dime store novels Gatsby has read. Gatsby also tells Nick that he is an Oxford graduate, a tradition that goes back generations in his family, and that he was decorated as a war hero in World War I by the country of Montenegro.
Nick believes none of it, but then Gatsby, like a good con artist, is able to produce the war medal and a photograph of himself at Oxford, which helps convince Nick the story is true. The story is a mix of truth and falsehood, though mostly falsehood, which is how a con man would operate.
In chapter 4, Jay Gatsby invites Nick Carraway to lunch in the city and tells him a fabricated story about his past in an attempt to ingratiate and impress Nick. While they are riding into the city, Gatsby asks Nick his opinion of him and remarks that he hails from a wealthy family in the Midwest. Gatsby then says that he was raised in America but educated at Oxford like the rest of his ancestors. Nick doesn't believe a shred of Gatsby's opening lies and wonders if there is something a "little sinister" about him.
Gatsby then undermines his entire lie by claiming that he grew up in San Francisco, which is not remotely close to the Midwest. He then claims to have lived like a "young rajah" following the war by collecting jewels, painting, and hunting big game animals in Paris, Venice, and Rome. At this point in the conversation, Nick finds Gatsby's story ridiculously hilarious and has to suppress his "incredulous laughter."
Gatsby then discusses his achievements during the war and says that every Allied government gave him a decoration, including the tiny nation of Montenegro. Just when Gatsby's story seems too outlandish to be true, he produces a small medal from Montenegro and shows Nick a picture of him alongside his Oxford peers. The medal and photograph seem to support his story, and Nick remarks that "it was all true." Nick is left with more questions about Gatsby's identity than answers, and Gatsby's attempt to prove his fabricated past leaves Nick more confused and suspicious of him.
In Chapter IV when Nick and Gatsby ride together into New York, Gatsby tells Nick about his past, in Gatsby's words "something about my life." He then tells Nick of his wealthy Midwestern family background and his Oxford education--a family tradition, he said. When his family died, he inherited "a good deal of money" that allowed him to travel throughout the European capitals where he collected jewels, hunted big game, painted, and tried to escape a sad, sad memory. His story continued as he recounted his military service in World War I and his decoration for heroism, a medal presented to him by Montenegro.
Throughout his recitation, Nick found Gatsby's speech and manner to be laughable; in fact, he had to make an effort to keep from laughing aloud. Nick found Gatsby's story to be beyond belief, including his birth in that famous Midwestern city, San Francisco. Nick was convinced that Gatsby's whole story was one lie upon another, until the end of it when Gatsby showed Nick two of his souvenirs: a photo of himself at Oxford and the medal from Montenegro. Both seemed very authentic, to Nick's complete astonishment, and convinced him that Gatsby's story was "all true." We find later that parts of it were true, at least.
Gatsby shared information about his life because he wanted Nick to think well of him. As Gatsby said, "I don't want you to get a wrong idea of me from all these stories you hear." As Chapter IV continues, we find out why. Gatsby wants a reunion with Daisy Buchanan, and he wants Nick to arrange their meeting.