Ponyboy expresses clearly his observations on their discussion of the sunset.
"It seemed funny to me that the sunset she saw from her patio and the one I saw from the back steps was the same one. Maybe the two different worlds we lived in weren't so different. We saw the same sunset."
Cherry and Ponyboy have an obvious and instant attraction despite the complex difficulties of their affiliations to the Soc's and the greasers. They are able to share personal observations on their lives and the restrictions they face despite their problems being so diverse. The significance of their discussion of the sunset is that firstly they realize that there are things bigger than the petty disputes which their lifestyles force them to be caught up in. Also, the sunset is a way in which despite the polar opposites of their existence, they do have some commonality as part of the bigger picture, and that both gangs exist under the same sun, in the same world, however different their respective parts are.
by agreeing on the basic fact that regardless greasers or socs, rich or poor, they still see the same sunset, it closes the gap between both social classes. If they are sharing the same sunset and wrold, they could share the same way of life---in peace
They realize that they are alike and have more in common than they first thought. They were both surprised to realize that they watch the same sunset and it created a bond.