Power weapon
Power weapons are a type of weapon in Warhammer 40,000. Power weapons look just like normal melee weapons, but what makes them actually useful is that they are sheathed with an energy field surrounding the blade. This energy field can in turn slice through even the toughest of armor.
Types of Power weapons
Crozius Arcanum
The signature weapon of Chaplains, the Crozius Arcanum is a mace encased in energy that serves as both a symbol of office and a weapon.
Power Sword
In a nutshell, the power sword is an example of power weapon technology applied to a sword. It's easily the most common power weapon (Seriously, fuck what Warhammer 40,000: Space Marine says about this, anyone with a functioning set of eyes and access to GW's own site can see it's bullshit), and is used not only by the Space Marines, but by the Commissariat, Inquisition, and Imperial Guard, who, likewise, often issue it to Sergeants and Officers. Most of the Primarchs who had swords used Power Swords.
A little known fact about Power swords is that if left turned on and dropped, the Power sword will continue to fall and bury itself in the earth until it reaches terminal velocity at the point it passes the planets theoretical centre of mass. It will begin to orbit the centre of the planet hollowing the centre out until it's power cell dies. Many Power swords have been lost this way. The sword's hilt would catch the ground and keep it from falling further into the earth.
Shock Mace
An older-model power weapon favored by the traitor legions, the Shock Mace is functionally a Crozius Arcanum.
Power Axe
More readily available in the armoury than Power Swords, and far more popular amongst the Loyalist Space Marines (According to some BS from the Space Marine game at least), Power Axes are single or double-bladed axes with their edges sheathed in energy. One would think that having technology available to them would better allow them to produce other types of power weapons, but the Adeptus Mechanicus are idiots like that. Power Axes are especially favored by the Space Wolves and some Chaos Lords.
Power Fist
One of the most iconic weapons of 40k, Power Fists are massive gauntlets which are encased within an energy field that breaks down molecular bonds when activated. They are intended to be worn with Terminator armour, but frequently you find people wearing Power Armour or even NOT wearing Power Anything wielding Power Fists. The God-Emperor of Mankind had a power fist on his left hand, which he used to famously put Leman Russ in his place. Russ later said that the subsequent headache was from the drinking contest they had.
Orks, in their looting tendencies, have taken to mimicking Power Fists as Power Klaws, which are like Power Fists except that they usually have 2-4 digits, and end in talon-like shears instead of articulated fingers. Commissar Yarrick infamously killed an Ork and used his Power Klaw to replace his severed forearm. Why the Commissariat has not censured him for using xenos weapons is not entirely clear, but they probably let it slide because he's such a badass.
Some variants of Power Fist are called Power Talons, which are basically Power Fists with the digits ending in razor sharp claws. You more frequently see them among Chaos Space Marines, but occasionally the Raven Guard or Space Wolves use them. The infamous Talon of Horus, used by Horus Lupercal to kill both Sanguinius and the Emperor and later looted by Ezekyle Abaddon, is an example of Power Talons with a bit more infamous history.
There has been some speculation on how successful it would be to incorporate Power Fists into truly epic highfives and brofists, but the AdMech has made it perfectly clear that to do so would be tech-heresy.
Lightning Claw
Lightning Claws are a quartet of razor-sharp claws affixed to a gauntlet, each blade of which is a small power weapon. The claws had different designs pre and post heresy, but they mostly function the same.
The pre-heresy design of the Lightning claws is that instead of blades being placed on the dorsal palm, the fingers on the glove of the claws are turned into power blades, giving the user a rather terrifying look. This is the wide-spread model that Chaos marines use since it's what they had when they fell back to the Eye of Terror.
The current design of Lightning claws are 3-4 giant power blades that are placed above the weapon's dorsal palm plating, akin to X-men's Wolverine.
They are normally used in pairs. Favored by Terminators and Chaos Raptors, Lightning Claws are a bit unwieldy, but are much more likely to land a damaging hit on a target when used by a trained user (in tabletop, this translates to re-rolling failed to-wound rolls). The Raven Guard in particular often employ Lightning Claws. Always remember to say "snikt" when using them and to take them off before attempting to masturbate or pick your nose.
Power Lance
A weapon used almost exclusively by the White Scars, Power Lances are energy sheathed lances which the White Scars use in charging their opponents on their bikes. You can imagine the results.
Thunder Hammer
Big fucking hammers that smash anything they touch. Unlike other power weapons, Thunder Hammer's only activate their energy fields upon contact with a target. This works like a flash capacitor, and utterly explodes whatever Thunder Hammers hit. Come in one-handed and two-handed varieties, but both functionally are the same weapon stat-wise.
Daemonhammer
It's a big thunder hammer that is consecrated with sacred oils and unguents to allow it to defeat Daemons.
Eldar Power Weapons
The Eldar have the knowledge to create power weapons as well: theirs are of a lighter, more elegant design, and are used almost exclusively by the Howling Banshee aspect warriors.
Eldar Power Sword
Used by the Howling Banshees, these weapons are of a more elegant design than their Imperial counterparts: they have a single edge and have a curve at the tip of the blade. Though being lighter, these weapons have more metal at the tip, allowing them to strike just as hard as an Imperial power weapon.
Mirrorswords
Somewhat smaller than, but otherwise identical to the regular power swords, these blades are used in pairs by the Exarchs of the Howling Banshees. The style that they are used in allows the wielder to deliver a far higher amount of blows on a target than with regular power swords.
Executioner
A glaive, this power weapon greatly enhances the power behind the user's blows, allowing the warrior to slice its enemies in half with ease. Exarchs of the Dire Avengers aspect use a similar, but lighter weapon for superior range over their enemies.
Powerblades
Attached to the user's forearms, these weapons grant the wielder the advantages of a power weapon while allowing the user to keep his hands free. Used mainly by Exarchs of the Warp Spiders aspect.