What is the purpose of Gatsby's active personality in Fitzgerald's The Great Gatsby?
The purpose of Gatsby's active personality, in that he has the liveliest parties in West Egg and beyond, is to get Daisy's attention, plain and simple. Gatsby started out poor and, therefore, could never truly attain Daisy's hand. When Gatsby got out of the service, he was determined to become rich and place himself near Daisy so she could rediscover him. Ironically, the biggest inkling about all of this obsession and loneliness comes from Jordan speaking of Gatsby and Daisy:
"I think he half expected her to wander into one of his parties, some night," went on Jordan, "But she never did. Then he began asking people casually if they knew her, and I was the first one he found. . . . He says he's read a Chicago paper for years just on the chance of catching a glimpse of Daisy's name." (80).
The irony of your question is that Gatsby doesn't really have an "active personality" at all. He is almost never seen at his own parties, but hovers behind the scenes in order to scout the crowd for Daisy. He has parties that are the epitome of recklessness from the "Roaring Twenties" in all of their glory, but never participates in them.