He's probably better off without it.
Before a decisive battle, the character tosses away his weapon's sheath (usually that of a sword) 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 the way during a fight, 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
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- 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 Anduril on the last ride to Mordor and vows that it shall not be sheathed again until the fight be over. Must've been really tedious riding all the way there with only one hand free for the reigns.
- Before his duel with Phrygiar Navaris in Captain's Fury in the Codex Alera, both Tavi and his opponent are noted as having their seconds hold onto the sheathes of their weapons because they would just get in the way.
- During the climactic chapter of Lioness Rampant, Alanna the Lioness discards her sheath while descending into the palace.
- In Asura's Wrath, Augus throws away his sheath when he draws Wailing Dark midway though his fight with Asura.
- In the Dragon Age: Origins trailer "Warden's Calling", the nameless Grey Warden throws away his sheath before charging at a horde of Darkspawn.
- It isn't focused on, but it is noticeable that Vergil disregards his sheath while running at Mundus at the end of the third Devil May Cry Despite his brave words, it's easy to interpret that that he is well aware of how insane this challenge is.
- In Final Fantasy X, Yojimbo's awesome-as-hell Zanbato move has him slowly draw his sword, dramatically throwing away the sheath.
- In Tales of Vesperia, Yuri Lowell typically does this at the start of every battle, flinging the sheath across the screen one-handed as he readies his blade.
- Yu Narukami tosses his katana's sheath away in one of his intro animations for Persona 4 Arena.
- 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.