Nick is the narrator because Fitzgerald needed a romantic, sensitive figure to paint a compelling portrait of Gatsby. Nick also has the classic attribute of a good narrator: he is an intimate bystander or observer of the events happening, so he can provide an eyewitness account, but he is not at the center of the drama.
As Nick himself notes, Gatsby, lower-class grifter and poser, is the kind of person he would normally despise. But Nick has the sensitivity to understand and convey what is going on beneath Gatsby's surface. He perceives Gatsby's greatness, and knows it doesn't come from his mansion or his lavish parties or the fancy cars he drives, but from his faithful and audacious pursuit of his dream. Nick admires this and sees Gatsby as the one beacon of light amid the "foul dust" that surrounds him. A less sensitive narrator—say Tom Buchanan—could easily have missed the desires that drove Gatsby and made him great. Nick's lyrical prose makes the story come alive and builds our sympathy for the novel's hero.
Further, Nick has the good or bad fortune to be a bridge between the major players in the story. He happens to live next door to Gatsby, to be Tom's college friend, and to be Daisy's cousin. He is near the center of the action but peripheral to it. He can tell us what happened with more objectivity (though he is not objective) than a character at the center of the drama.