He's probably better off without it.
Before a decisive battle, the character tosses away their weapon's (usually a sword) sheath to demonstrate that he will not back down from the fight. A darker implication of this gesture is that the character realizes that his chances to survive are slim and he won't have a chance to sheathe his weapon ever again.
Aside from the symbolic meaning, putting away your sheath has a purely practical rationale: the sheath usually gets in way when fighting, and the enemy can grab it to restrict your movement. Contrast Sheath Strike
As mentioned, this works best with bladed weapons, since more modern ones, like firearms, lack an exact analog to a sheath. Throwing away a holster just doesn't look as dramatic
- On Gor, a Warrior carries his sword in a baldrick. While on the march it's slung over the right shoulder (assuming the Warrior is right handed) with the sword on the left hip, to give some security; but when preparing for battle it's slung over the left shoulder so it can be quickly discarded.
- Not a literal example, but in The Lord of the Rings: Return of the King (both the book and the movie), Aragorn unsheathes Narsil on the last ride to Mordor and vows that it shall not be sheathed again until the fight be over.
- From the Scottish folk song "Gallant Murray":
"His good sword he now has drawn it, Video Games
And he's flung the sheath away"
- John Singleton Copley invoked this trope when talking about the American Revolution: "When the sword of rebellion is drawn, the sheath should be thrown away."
- At the start of his (fatal) duel with Miyamoto Musashi, in a rage over Musashi's late arrival, Sasaki Kojirō supposedly drew his katana and threw the sheath away, possibly into the ocean. Musashi turned this around by observing that Kojirō must not be planning to win, because otherwise he would need the sheath when the fight was over.
Will go under Weapons and Wielding Tropes
and Body Language