Short answers, pulled from the story.
The Battle of the Pelennor Fields is the largest battle in Tolkien's War of the Ring, fought on the townlands between Minas Tirith and the River Anduin. It pitted the combined forces of Gondor and Rohan against Sauron's army from Mordor, including Haradrim, Easterlings, orcs, and trolls. The battle takes place on the 15th of March in Tolkien's timeline and ends at sunset with no living enemy remaining on the field.
The Witch-king is killed by two blows working together. The hobbit Meriadoc Brandybuck stabbed him behind the knee with a Barrow-blade from the ancient kingdom of Arnor, enchanted against the forces of Angmar. Éowyn, Théoden's niece, then drove her sword between his crown and mantle. Both weapons were destroyed in the act, fulfilling Glorfindel's prophecy that the Witch-king would not fall by the hand of man.
Rohan contributed a 6,000-strong cavalry army, the Rohirrim. They were described by Tolkien as thrice outnumbered by the Haradrim alone. The Rohirrim reached the battle undetected because the Drúedain guided them through the hidden Stonewain Valley of the Drúadan Forest, bypassing Sauron's lookouts.
Scholars have identified the Battle of the Catalaunian Fields, described by the historian Jordanes, as a key source; scholar Elizabeth Solopova notes Tolkien repeatedly referenced that account, and the death of the Visigoth king Theodoric I closely parallels Théoden's death. Tolkien also served in the Battle of the Somme in 1916, and C. S. Lewis, himself a veteran, remarked that Tolkien's war writing captured the quality of the war their generation knew.
The battle is the centrepiece of The Lord of the Rings: The Return of the King (2003). Jackson said he drew visual inspiration from Albrecht Altdorfer's 1529 oil painting The Battle of Alexander at Issus, depicting events of 333 BC. The film's battle scenes were described as the most spectacular ever filmed, though the climax involving the Army of the Dead was also called an oversimplified resolution by some critics.
Tolkien scholar Tom Shippey traces the cock-crow, heard just as Rohan's horns sound, across multiple traditions in Western literature, including the denial of Christ by Simon Peter and the Norse tale of King Hadding. Shippey argues the combined signal of cock-crow and warhorns conveys that dying undaunted is no defeat, a Northern European idea that predates Christianity.