This famous incident occurs in Chapter Five of this great novel. Let us remember the context: Gatsby has met with Daisy for the first time since he left for war, and now is showing her his mansion and obviously showing off his incredible wealth. The scene where he begins randomly throwing them into the air in my opinion is meant to be another extravagant demonstration of his wealth and importance so that he can show Daisy that he has completely transformed from being the poor individual she knew before the war. What is important to note is Daisy's reaction to the barrage of shirts that come from England:
"They're such beautiful shirts," she sobbed, her voice muffled in the thick folds. "It makes me sad because I've never seen such--such beautiful shirts before."
Let us remember that anything coming from England was thought to be that much better and therfore more expensive. Daisy's reaction and her tears seem to symbolise an understanding of what she has given up by choosing to marry Tom over Gatsby. It also gives us a clear insight into Daisy's character. She is somebody who places an inestimable value on wealth and its conspicuous consumption. The sight of all of these exquisite shirts flying through the air produces tears in her because money is what is important to her. Therefore this shirt scene is important for what it reveals about character and also for what it tells us about Daisy in particular, and her thoughts and feelings about Gatsby at this stage.
I'd agree here with the 3rd post - The shirt scene demonstrates the notion that Gatsby both understands and participates in the same materialistic fetishism that Daisy has adopted.
It is interesting to think about how each of them got there, however, having given up on love (each other) so long ago. The shirts represent both a strange redemption of a dream (wherein these two can see themselves together) and the distance that each has come from the innocent ideals of youth (wherin there was no need for so much wealth).
Another intepretation of the shirt scene is to see it as a moment of realization. Daisy sheds tears, saying the shirts are so beautiful, but seems to be crying for all the time that was lost. She could have been with Gatsby, whom she loves, instead of with Tom, whom she does not. Those shirts represent a wasted life.
I with the posts above and would add something about the fact that the shirts are all brightly colored. Traditional business men of the time would have more likely worn a stark white dress shirt and tie, but Gatsby's shirts are bright and showy -- another reference to his "new" wealth as opposed the more staid and traditional apparel of the "old" established wealth. Just as his parties and his car are flashy, so is his wardrobe.
The scene in which Gatsby thinks to impress Daisy is, indeed, pathetic. Against all the things that he could do to make Daisy think well of him, when Gatsby chooses to display all his English shirts, the implication is certainly that Gatsby understands that Daisy is purely materialistic. When she places her face in them and cries--oh, brother! How pathetically shallow is this?
My feeling about this scene is that it makes me feel sorry for both of these characters. I feel sorry for Gatsby because he feels that having all these shirts makes him in some way a better man. I feel sorry for Daisy because she seems to agree. The shirts matter to her. This shows how pathetic they both are.