This question asks for inference as there is no direct explanation offered in the text. While she sobs with her face buried in the shirts, Daisy says, "It makes me sad because I've never seen such - such beautiful shirts before."
Her sadness may stem from regret. When she married Tom she only married him reluctantly. Jordan recounts the story of that marriage to Nick, describing Daisy's drunken efforts to break off the wedding on her wedding day. She goes through with the wedding and seems to love Tom, but she receives a letter that she clings to on her wedding day, presumably from Gatsby, and her heart is clearly not fully invested in the idea of being married to Tom.
The "what if" regret may be what we see as Daisy cries into Gatsby's shirts. What if she had waited for Gatsby to return from the war? What if she had followed her instincts and refused to marry Tom? Would she be happier with Gatsby?
Now that she sees how well-off Gatsby is, she can envision a life of romance and love and wealth with Gatsby that may exceed what she has had with Tom. The shirts represent this possibility, which she chose against in marrying Tom.