This is the Anduril, Flame of the West, reforged for Aragorn by the elves from the shards of Narsil kept at Rivendell. It is the sword that Aragorn will wield once he becomes King.
At the end of the second age of Middle-earth, Narsil's blade was shattered, as Elendil fell during the Last Alliance of Elves and Men in the great battle against Sauron, creating the Shards of Narsil. Isildur, Elendil's son, then used the broken hilt of Narsil to cut the One Ring from Sauron's finger, breaking the bonds of his power. The Shards were kept in Rivendell, the house of Elrond. Legend told that the sword would one day be reforged and the King would return.
The inscription down the length of the blade on both sides is in the Tolkien language of Quenya, written in the runes of Eregion, that say "Nányë Andúril i né Narsil i macil Elendilo. Lercuvanten i máli Mordórëo". This translates to "I am Andúril who was Narsil, the sword of Elendil. Let the thralls of Mordor flee me."
The blade inscription features runes framed by stylized symbols of the Sun and the Moon, which represent An'rion and Isildur, the sons of Elendil, and seven symbolic stars that represent Elendil, who died wielding Narsil in battle against Sauron. Inscribed on the pommel are runes in the Elven language of Sindarin that say "Narsil essenya, macil meletya; Telchar carneron Navarotesse". This translates to "Narsil is my name, a mighty sword; Telchar made me in Nogrod"