He drew out his sword, and they saw that the blade was indeed broken a foot below the hilt. 'Not much use is it, Sam?' said Strider. 'But the time is near when it shall be forged anew.'

(LoTR, I-10)

`I was the herald of Gil-galad and marched with his host. I was at the Battle of Dagorlad before the Black Gate of Mordor, where we had the mastery: for the Spear of Gil-galad and the Sword of Elendil, Aiglos and Narsil, none could withstand. I beheld the last combat on the slopes of Orodruin, where Gil-galad died, and Elendil fell, and Narsil broke beneath him; but Sauron himself was overthrown, and Isildur cut the Ring from his hand with the hilt-shard of his father's sword, and took it for his own.'
...
From the ruin of the Gladden Fields, where Isildur perished, three men only came ever back over the mountains after long wandering. One of these was Ohtar, the esquire of Isildur, who bore the shards of the sword of Elendil; and he brought them to Valandil, the heir of Isildur, who being but a child had remained here in Rivendell. But Narsil was broken and its light extinguished, and it has not yet been forged again.

(LoTR, II-2)

The Sword of Elendil was forged anew by Elvish smiths, and on its blade was traced a device of seven stars set between the crescent Moon and the rayed Sun, and about them was written many runes; for Aragorn son of Arathorn was going to war upon the marches of Mordor. Very bright was that sword when it was made whole again; the light of the sun shone redly in it, and the light of the moon shone cold, and its edge was hard and keen. And Aragorn gave it a new name and called it And�ril, Flame of the West.

(LoTR, II-3)

...and the sword of Elendil filled Orcs and Men with fear, for it shone with the light of the sun and of the moon, and it was named Narsil.
...
There in the valley of Gorgoroth Anarion son of Elendil was slain, and many others. But at the last the siege was so strait that Sauron himself came forth; and he wrestled with Gil-galad and Elendil, and they both were slain, and the sword of Elendil broke under him as he fell. But Sauron also was thrown down, and with the hilt-shard of Narsil Isildur cut the Ruling Ring from the hand of Sauron and took it for his own.
...
Thus [after the Disaster of the Gladden Fields] Narsil came in due time to the hand of Valandil, Isildur's heir, in Imladris; but the blade was broken and its light was extinguished, and it was not forged anew. And Master Elrond foretold that this would not be done until the Ruling Ring should be found again and Sauron should return; but the hope of Elves and Men was that these things might never come to pass.
...
Here let it be said that in those days the Heir of Isildur arose in the North, and he took the shards of the sword of Elendil, and in Imladris they were reforged; and he went then to war, a great captain of Men. He was Aragorn son of Arathorn, the nine and thirtieth heir in the right line from Isildur, and yet more like to Elendil than any before him.

(Silm, OF THE RINGS OF POWER AND THE THIRD AGE)

Narsil - The sword of Elendil, made by Telchar of Nogrod, that was broken when Elendil died in combat with Sauron; from the shards it was reforged for Aragorn and named Anduril. 364-5

nár - 'fire' in Narsil, Narya; present also in the original forms of Aegnor (Aikanáro 'Sharp Flame' or 'Fell Fire') and Fëanor (Feanaro 'Spirit of Fire'). The Sindarin form was naur, as in Sammath Naur, the Chambers of Anárion), Sindarin Anor (cf. Minas Anor, Anorien).

sil- - (and variant thil-) 'shine (with white or silver light)' in Belthil, Galathilion, Silpion, and in Quenya Isil, Sindarin Ithil, the Moon (whence Isildur, Narsil; Minas Ithil, Ithilien). The Quenya word Silmarilli is said to derive from the name silima that Fëanor gave to the substance from which they were made.

(Silm, Appendix)