Big and Carrie became "friends", but Big didn't like Carrie seeing others. Carrie still had feelings for Aidan so they got back together. Aidan proposed to Carrie, Carrie said yes, but she didn't want to get married now. Aidan moved out. Big moved from New York.
After all, seasons change. So do cities. People come into your life and people go. But it's comforting to know the ones you love are always in your heart.