Gandalf and Aragorn go off high above the city and find a seedling of the White Tree, which Aragorn then plants in Minas Tirith in place of the dead tree. Soon after, Arwen, daughter of Elrond of Rivendell, as well as Celeborn and Galadriel come to Minas Tirith, and Aragorn marries Arwen.
other Tolkien of mine:
This scene in the movies is one of the few times I have ever openly wept during a movie.
Especially the very end when King Elessar looks at the kneeling hobbits and says quietly,
"My friends. You bow to no one"
And then the greatest King of Men since Elendil himself knelt before four simple hobbits from the Shire, and all of Middle Earth followed suit.