In the gift of the magic what happens during the story's exposition?

I suspect you mean O Henry's classic story 'The Gift of the Magi'.

In the exposition of the story Mrs. DELLa Young - wife to Mr. James Young - finds that it is Christmas Eve, and she has very little money with which to buy her young husband a Christmas present. The two young marrieds are living in a cheap apartment in New York, and Mr. Young's wages have recently been reduced. But DELLa very much wants to buy her husband something special this Christmas - they love each other so very much.