Assassin

Assasins are highly trained agents who are dispatched to kill a specific, high value target, usually using stealth and cunning. Many have their own methods of dealing with their target, such as using poisons, blades, or ranged weapons, or simply brutal cunning, though they all usually involve being very discreet and virtually undetectable or tracable, allowing them to escape once the job is done as if they were never there.

We also keep saying usually because there's a specific breed of assasins who likes to instead use the stealth of a Baneblade and the cunning of a Carnifex, all the while having the subtly of an Khornate Berzerker, to kill their target.

Imperial Assassins

Imperial assassins are operatives who function under the command of the Officio Assassinorum, a branch of the Imperium. They are usually 'recruited' (kidnapped) at a young age, generally from orphans, and occasionally certain physical properties are required (i.e. psychic blanks needed for the Culexus temple). The Assassinorum's relentless training and biological augmentation of these children through their lives turns them into the perfect weapons. By the time they are ready for active duty, they are as strong and tough as a Space Marine, faster than an Eldar Banshee, more deadly in close combat than a Grey Knight Grand Master, and more accurate at range than just about everything.

Imperial Assassins will be from one of the six 'Temples' of the Officio Assassinorum:

• The Callidus Temple
• The Culexus Temple
• The Eversor Temple
• The Vindicare Temple
• The Venenum Temple, who focus on poisoning people.
• The Vanus Temple, who emphasise information-gathering, clean kills, and accidental/deniable deaths.

The last two are less well known about; they don't have models, and, since they're largely 'behind the scenes' killers, don't really fit into tabletop 40k.

All assassins are equipped with 'synskin', a second skin that is sprayed on before a mission, which hardens and forms a perfectly fitting excuse for the latex stealth suit trope, which only exists so that Callidus assassins could be girls in latex zentai suit which dissipates the kinetic energy from incoming projectiles, allowing them to survive shots that could have killed them otherwise, and they possess such incredible reflexes that they can literally dodge incoming fire.

The four main temples chiefly differ in equipment and tactics:

• The Callidus temple uses the art of camouflage and subterfuge to achieve their goals. Their operatives use a drug called 'Polymorphine' to actually change the shape of their bodies. This, combined with impeccable knowledge of the cultures and mannerisms of the many species of the galaxy, allows them to believably impersonate anything, from a hulking, brutish Ork, to a beautiful human woman. Due to the nature of their work, the Callidus tend to be the most sociably able of the four assassins. They are frequently equipped with a C'tan phase blade, which can slice through Adamantium like butter, and causes instant death to any unfortunate enough to feel its edge. This is complemented by the ranged fury of the 'Neural Shredder', a small pistol that affects a large conical area in front of the barrel. Rather than damage foes depending on their physical toughness, it affects them differently depending on how mentally resolute they are, cowardly foes will fall like chaff to this weapon, whereas courageous enemies can shrug off its effects. Callidus are also significant psychological tools, if an enemy knows that any one of his 'allies' right next to him could be a Callidus, who knows how he may react?
• The Culexus temple recruits solely from phychic 'blanks'. Blanks are beings that have no presence in the Warp (essentially soulless). Blanks cause agony to nearby psykers, and can even kill weaker ones at close range. Due to this Culexus assassins are generally deployed when the oppositions force features many psykers (i.e. Eldar). The presence of a blank chills the soul of nearby non-psykers, and as such, they are generally avoided by all that don't absolutely have to be in contact with them. Culexus assassins are equipped with the 'Animus Speculum', a skull shaped helm that can concentrate the operatives anti-warp signature and launch bolts of energy across the battlefield, which shred right through flesh and armour like paper. When allied psykers are near, the Culexus's anti-warp energy increases, allowing him to launch more bolts from his Animus Speculum. They also possess the 'Etherium', a device that lets you find a flying castle allows the Culexus to step out of phase with the material world, making the opposition question what they're aiming at is really there; only the most resolute foes dare to fire at the mysterious shadow of despair stalking the battlefield. The Culexus assassins are also equipped with a 'Psyocculum', a device which allows them to see the flow of the warp overlapping with this reality; through this vision, psykers shine like a fire, allowing the Culexus to easily find and impeccably target enemy psykers.
• The Eversor temple firmly believes that the sledgehammer is mightier than the scalpel. Rather than quickly taking out a few key targets, the Eversor annihilates vast numbers of enemies in a whirlwind of gore. When sent into battle, an Eversor is pumped full of 'Frenzon', an extremely powerful aggression raising drug, that allows the operative to unleash a flurry of blows before the enemy even knows they are under attack. Outside of combat Eversors are heavily tranquilized to the point where they are essentially in an induced coma. This means they are human only in classification, their minds filled with nothing but desire to destroy the enemies of the Emperor. Eversor assassins are equipped with a 'Neuro Gauntlet', a vicious weapon that consists of 5 small power blades mounted on the Eversor's fingers. For ranged combat they have the 'Executioner Pistol', a modified bolt pistol that fires highly penetrating, envenomed rounds that can tear through any flesh and armour with frightening ease. In case they encounter something too big to simply rip to pieces, they possess Melta-bombs to ravage enemy Armour.
• The Vindicare temple specialises in long-ranged combat, with their operatives being the greatest snipers in the Imperium, and probably the entire Galaxy. Vindicare training concentrates on patience (as the assassin may have to remain still for days on end to attain the perfect shot), and emotional repression, lest the Vindicare find himself unable to pull the trigger at the vital moment. They have also been taught to focus their senses, allowing them to pick out a single target no matter how many allies it may be surrounded by. Vindicares are equipped with the finest sniping weapon known to man, the Exitus Rifle, a veritable masterpiece of firearm. Powerful enough to tear through Tactical Dreadnought Armour, and accurate enough to hit a Bloodthirster in the eye. This is paired with the Exitus pistol, smaller and more wield-able, but no less deadly than the rifle. They also have access to special ammunition, such as bio-acid Hellfire rounds that eat through living tissue, shield-breaker rounds that permanently disrupt force fields, and anti-vehicular rounds that can punch right through a Land Raider. They also possess 'Blind' grenades, grenades that explode with a brilliant flash of light and infra-red radiation (so heat-vision won't work), that dazzle assaulting foes and ensure they can't catch the Vindicare off guard.

• The Death-cult assassins may be considered Imperial Assassins, even though they are not under the Officio Assassinorum, many inquisitors employ them for their skill with the twin power weapons they carry. They are able to strike several deadly blows on a foe very quickly. Whilst still dangerous foes, they in no way compare to 'official' Assassins.

The other guy

The entire concept of the Assassins evolved from a single entry in the original Second Edition army list for an Imperial Assassin, who could take any combination of wargear and a special card exclusive to him, Polymorphine, which allowed him to disguise himself as another model. This duly proved completely broken since there was no specific rule to say a Gretchin couldn't be an Imperial Assassin wearing Terminator Armour and riding a bike, and abuses of the Polymorphine Wargear card (especially those involving Vortex Grenades) seem to have been a large part of the reason why the later version of it made it exclusive to the far more limited Callidus Assassin.

TL:DR: They evolved from cheating.