The Nightfall Sword is a sword crafted using Ender Golem Horns and it's stronger than a iron sword. When the player crafts this sword for the first time the achievement It's cutting edge! will pop up. Enderminions and Looters can also use this sword.
If the player is carrying the Nightfall Sword and is wearing at least 1 piece of the Nightfall Armor, he'll get a Damage Boost buff.