Money is a very important element in this story, because it drives a lot of the frustrations and unhappiness of the characters.  Ethan's mill never makes very much money, so he doesn't have the freedom to travel, go to school, hire a nurse for ailing relatives, or have many comforts.  If he had money, it would offer him the luxury of leaving Zeena with some, and going off to pursue his dreams and hopes.  He would not have had to go back to the mill from school to tend his parents, and he could have gone back to school after they died.

Money also brings Mattie to them--she is poor, and needs a place to stay and eat.  She wouldn't need to rely on distant relatives to help if she had more money.  Money also intensifies the conflict and drama.  When he goes to town to get more money, he lies about having gotten it, in order to hide his affection for Mattie.  Zeena believes him and takes the long trip that leads to Mattie and Ethan acting on their feelings for one another.  That is the crux of the story; Ethan's lie about money created a very difficult situation for all of them.

I hope that those thoughts helped; good luck!