The James Gatz story is important for at least two reasons. First, readers are trying to keep track of truth and lies in this story, and the James Gatz story is a guaranteed truth as it comes from our author, not a biased character.
Second, this story of his background gives merit to the idea that Gatsby is in pursuit of finding his identity. A name change suggests a complete and total change of a person, and we can see that as the James Gatz character was not too successful, while the Jay Gatsby character is extremely successful. At one point, Nick narrates,
"It was James Gatz who had been loafing along the beach that afternoon in a torn green jersey and a pair of canvas pants, but it was already Jay Gatsby who borrowed a rowboat, pulled out to the Tulomee, and informed Cody that a wind might catch him and break him up in half an hour."
James Gatz went from a 17-year-old who lacked confidence to a 17-year-old entrapaneur taking a risk to initiate conversation with an obvious wealthy man who had no concept of a potential upcoming gale.
Later Nick notices about the emerging Gatsby:
"But his heart was in a constant, turbulent riot. The most grotesque and fantastic conceits haunted him in his bed at night."
The new Gatsby character was taken with his imagination and believed in a glorious and fantastic possible future.
This entire section is important because Gatsby is an everyman in many ways. All mankind dreams about what more could come in their lives. The restless discontent of Americans with the status quo is ever present. This story of James Gatz demonstrates that in Gatsby's life, there was a defining moment which forever changed him from the sweet lakeside boy to the ambitious American dreamer.