In the film "The Return of the King," Aragorn is crowned King after the One Ring has been destroyed.
Aragorn is the heir of Isildur and the rightful claimant to the thrones of Gondor and Arnor. For much of the trilogy, he lives as a ranger under the name Strider and hesitates to embrace his royal heritage because of his ancestor Isildur's failure to destroy the Ring.
After Frodo and Sam's quest succeeds and the Ring is destroyed in Mount Doom, Sauron's power collapses. Aragorn's role in uniting the Free Peoples and leading the battle at the Black Gate helps secure victory. He is then crowned King Elessar, beginning a restored royal line and a new era for Gondor.
The coronation is followed by Aragorn's marriage to Arwen, daughter of Elrond. Théoden's successor, Éomer, is separately crowned King of Rohan, which is a common source of confusion when recalling the film's closing celebrations.