In chapter five, Gatsby opens two large cabinets in his room to show Nick and Daisy his shirts. These shirts are "piled like bricks in stacks a dozen high" before Gatsby starts pulling them out.
This is significant because it shows that money is no object to Gatsby. He has amassed such a great fortune that he can afford any item he desires. This is further reinforced by the fact that he has a personal buyer in England who sends the shirts to him. He is literally so rich that he can pay someone to do all of his shopping.
In addition, the shirts are significant because he is deliberately displaying them to Daisy. Believing that she is materialistic, Gatsby thinks that this display of his wealth and style will help to win her back. This is merely one of his tactics in his quest to reignite her love for him. Daisy's reaction validates this idea. By sobbing and commenting on the beauty of his shirts, Daisy proves that Gatsby is right: she is indeed materialistic, making this display a small triumph for Gatsby in his mission to win her back.
In my opinion, Gatsby's shirts are significant because they show just how far Gatsby is willing to go to get Daisy. In addition, her reaction to them, in my opinion, shows how shallow she is.
The whole house and the shirts and everything are Gatsby's attempt to get Daisy to love him. He wants to show her just how rich and classy he is. He is so classy that he even has his shirts sent over from England (and lots of them).
When Daisy sees them, she breaks down and cries. If she were a more genuine person, you would think she would be overcome by emotion on seeing Gatsby or on hearing him say something. But instead, what gets her is his material possessions.
I agree that the shirts are signs of Gatsby's wealth. Just as the wealthy people leaving the party earlier in the story didn't care that they had wrecked their cars, Gatsby uses the flippant gesture of throwing his shirts to show just how much disposable wealth he has.
We also need to consider what exactly shirts meant in the Fitzgerald era. Shirts were not two for $10's at the local super-mart and average people didn't own fifteen pairs of shoes. The statement he is making is the same as the act of throwing twenty dollar bills out the window of a car.
Gatsby's shirts show that materialism brings Gatsby's enjoyment. By Daisy's crying, we can tell that Gatsby's shirts are extensively luxurious and that he must expend much time and money in choosing his clothing.