Narsil is the sword that was broken and later reforged as Andúril in J.R.R. Tolkien’s legendarium. Elendil carried Narsil during the Last Alliance of Elves and Men, and the sword broke when he fell while fighting Sauron at the end of the Second Age.
Isildur used the broken sword’s hilt-shard to cut the One Ring from Sauron’s hand. The shards were preserved by Isildur’s heirs, eventually becoming a symbol of the lost kingship of Arnor and Gondor. Aragorn carries the shards after the Fellowship leaves Rivendell.
Before the Fellowship travels south, Elrond has the sword reforged. Aragorn receives the new blade under the name Andúril, Flame of the West. Narsil is distinct from Glamdring and Orcrist, which were ancient blades found in a Troll hoard, and from Sting, the smaller sword carried by Bilbo and Frodo.