What part of his past is Gatsby trying to recapture?

Gatsby is trying to recapture the moment in time five years past when he and Daisy first fell in love. As Jordan tells the story to Nick, who tells it to us, Daisy and Jay met 1917, during World War I. Gatsby, a young lieutenant, was stationed at Camp Taylor, near Jordan and Daisy's homes. Daisy was the most popular of the girls. One day, as Jordan walked past, Daisy beckoned her to the porch and introduced her to Jay Gatsby. As Jordan recalls it, the 

officer looked at Daisy while she was speaking, in a way that every young girl wants to be looked at sometime, and because it seemed romantic to me I have remembered the incident ever since.

Jordan later heard "wild rumors" that Daisy's mother prevented her from going to New York to see off a young soldier, presumably Gatsby.
Gatsby wants to go back to that magical moment in 1917 when he and Daisy were in love.  However, Daisy has moved on. She is married and has a child. Nick tries to tell Gatsby he can't turn back the hands of time, but Gatsby refuses to believe it. He thinks Daisy will leave Tom, so that he and Daisy can start all over again.