The Midnight Rapier is a melee blade bought at the Chilly Smith. Its base power depends on the corruption and rapier skill of the champion. It's notable for being the most powerful weapon in the game under the right circumstances, beating even the Scarred Blade. It's also the only weapon where the champion can only get one, even through different ascensions.
The Midnight Rapier was an idea originally by Zavos, but was developed, fine-tuned, and coded by Foxwells.
It's possible for the rapier to have negative power, if the champion is pure enough and has high corruption tolerance.
The rapier is the most powerful weapon in the game, surpassing the Scarred Blade used by a champion with 100 corruption by 4 points provided the champion has 100 corruption and maximum rapier training.
With training and 91 corruption, but the Scarred Blade with 100, it's ahead by 1 point.
Without the rapier training but 100 corruption, it's less powerful by 2 points.
At 91 corruption and no training, but the Scarred Blade with 100, it's behind by 5.
The power of the rapier is, in Foxwells' words, an accident. Zavos' original idea was pitched as a rapier for those who can't get Raphael's training, but was also supposed to be weaker than Raphael's Rapier. Foxwells found that confusing and made the Midnight Rapier's power based on corruption and rapier training.
Foxwells didn't intend to include rapier training in the power calculation, nor did he want to, but figured Kitteh6660 would code it if he didn't.
The Midnight Rapier was originally going to be an item obtained exclusively through an NPC, after defeating them in battle multiple times. This idea was scrapped with the revamp of the Chilly Smith.
Weapons are equippable items used to boost attack, among other effects.