The shirts symbolize Gatsby's wealth and demonstrate his rather ostentatious style. When Daisy looks at them all, she is overwhelmed and brought to tears.
The shirts can be seen as a representation of an image or an ideal, one which she and Gatsby seem to share regarding wealth, glamour and self-presentation.
The shirts themselves mean little. They are merely cloth. What they represent is quite meaningful, however, as Daisy and Gatsby both prize appearances and fantasy over substance and reality.
This notion is borne out by the nature of their liaison, which consists of a series of conversations about how great things will be in the future, and also borne out by the fact that Daisy does not leave her husband. The affair between Daisy and Gatsby is, ultimately, simply a show. It is a play at a romance, an image of love.
The shirts then are related to the idea that appearances are important to these two. It is the image that they respond to, not the substance of the thing(s).