According to the movie trilogy's official publicity material, Hadhafang (whose name is a newly-coined Sindarin word meaning "Throng-cleaver"), once belonged to the Elven Princess Idril, who wed a mortal man and bore Earendil, the father of Elrond who in turn was father to Arwen. (This is another departure from Tolkien's work. In fact, as written in The Silmarillion, both Idril and Earendil were Half-elven.) Before Arwen's birth, Elrond wielded Hadhafang at the end of the second age of Middle-earth, during the Last Alliance of Elves and Men in the great battle against Sauron on the slopes of Mount Doom.
Later his daughter, Arwen, used Hadhafang when she aided Frodo in his escape from the Ringwraiths. Inscribed on the blade are runes in the Elven language of Sindarin that say "aen estar Hadhafang i chathol hen, thand arod dan i thang an i arwen." Which transfers to "this blade is called Hadhafang, a noble defense against the enemy throng for a noble lady." In the Elven language of Sindarin "Arwen" actually means "Noble (or Royal) Woman".
Like all of the props used in the Lord of the Rings movie trilogy Hadhafang was manufactured by Weta Workshop.