Gramr is the legendary sword forged by Odin and gifted to Sigmund, later used by Sigurd to kill the dragon Fafnir. It is the sword that Senua is tasked with reforging (through completing several trials) so that she can use it to defeat Hela.
According to Druth's narrations, Gramr was made from the remains of the sword given to Sigmund by Odin. The sword was trapped in a tree and would be a gift to anyone who could remove it from the tree; only Sigmund was capable of freeing the sword. When King Sigguir captures Sigmund and his brothers, he takes the sword for himself. Years later, when Sigmund and his son Sinfjotli are being buried alive by Sigguir, Sigmund's sister tosses a bundle of straw containing the sword into the grave, and Sigmund is able to escape the grave with his sword.
Sigmund uses the sword in many battles thereafter, but in his final one, Odin comes to the battlefield. Odin raises his spear against Sigmund, and Sigmund struck at the spear, but the sword was shattered. Sigmund, realising this was Odin, accepted his fate, telling his wife that their unborn son will reforge the sword.
The son of Sigmund, Sigurd, plans to slay the dragon Fafnir if the dwarf Regin forges a strong sword for him. Sigurd's mother still has the pieces of Sigmund's sword, and Regin reforges the sword. Sigurd kills Fafnir by plunging the entire blade into the dragon's body.
Hellblade: Senua's Sacrifice
Senua follows the vision of Dillion to a large tree on a beach, where the sword is firmly embedded in the roots. Senua attempts to pull it out, but is unable to. Druth's voice tells her of that sword, Gramr, which is capable of killing a god; it appears intact, but was shattered into several pieces long ago. Druth tells her that she can reforge the sword if she completes the trials of Odin.
After completing all four trials, Senua is able to pull the sword from the tree and use it against enemies. She uses it in her fight against Fenrir and then in the final battle in Hela's Sanctum.
In her final encounter with Hela, Senua is overwhelmed by enemies and eventually cannot fight anymore. She drops Gramr, which Hela picks up. Upon realizing that she cannot save Dillion, Senua tells Hela that she should just kill her; Hela does so, running Senua through with Gramr.
What happens to the sword afterwards is unknown; in the ending cutscene, it is not in Senua's sword hilt.
In combat, Gramr has the same capabilities as Senua's original sword, with a few exceptions. Senua is able to charge her heavy attack to deal extra damage to enemies, though this leaves her vulnerable to attack for a short window. If she parries the attack of an enemy covered in shadow, she will bring it out of the shadow much as she would if she were using her focus.