In The Great Gatsby, why does Gatsby throw huge expensive parties for people he does not even know?
To a large extent, it's a sign of insecurity. Like a lot of members of the new rich, Gatsby is acutely aware that the old money families look down on those who worked for their wealth rather than inherited it. As someone from a humble Midwest background who made his fortune from various criminal enterprises, Gatsby feels like he doesn't truly belong among the social elite, no matter how much money he has. Lavish parties and other ostentatious displays of wealth are a way for Gatsby to try and find a place for himself in high society, even if it's all just on the surface. If he has to buy his way in, then so be it. Although the East Eggers may look down on Gatsby and his kind, many of them will still attend his parties. Then as now, money talks.
His parties are also an outward sign to Gatsby that he's made a clean break in life. The parties, and all the other trappings of his enormous wealth, allow him to place a veneer of respectability over a life that, up until now, has been anything but. Throwing lavish parties and playing the gracious host confer a sense of respectability on Gatsby, making people think that he's just like any other legitimate businessman with a taste for the finer things in life. For Gatsby, as with many people in this materialistic age, it doesn't matter what you are; what matters is what people think you are.
In The Great Gatsby, Jay Gatsby throws parties to fill a void in his past; to exercise his present power; and to impress the one woman he had ever loved, for whom he wasn't good enough. Jay Gatsby began life in humble circumstances, tried to improve his situation, met wealthy, pampered Daisy and fell in love. She didn't marry him because he wasn't good enough and could neither appreciate nor provide all the comforts she was accustomed to.
When Gatsby made his fortune through dishonest means, he began surrounding himself with the pomp, luxury and social acceptance he never had and which Daisy had demanded of him. He entertained a secret hope that Daisy would find her way into his world again. He threw lavish parties to create what Daisy demanded and to exercise the power of his vast wealth, knowing all the while that people had heard rumors about his business dealings and the source of his wealth and didn't really think of him as a friend: To the social circle, Gatsby was only a good time, but the people partying at his home gave him what he was looking for anyway.