Facsimile Constructs are artificial copies of existing beings, such as humans or Transformers. Their specifications vary across different uses and continuities.
Marvel Comics continuity
In order to more easily blend in with humanity, Wheeljack designed and installed "Facsimile circuitry" in all the Autobots. Remarkably low-tech for Ol' Wheels, the technology consisted of little more than "dummy drivers" that popped out of the driver's seats in vehicle mode. The original versions seemed unable to move their lips while "talking" or turn their heads, and were installed with a decidedly unnatural swivel joint in the arm so that they could hand over their Blackrock credit cards to pay for gasoline. Later versions of the technology were installed in the Autobot Micromasters when they arrived on Earth, but despite having a greater range of movement they still were largely incapable of fooling a human in close quarters.
Another form of facsimile construct was frequently used on Cybertron and sometimes on Earth to mimic full-sized Transformers. They were mindless drones but could be programmed with basic responses. They are also used as decoys and in training exercises to represent enemies.
When planning Operation: Volcano, Facsimile Constructs were used by the Wreckers in training exercises to represent their Decepticon opponents. They were also used as bait for the Decepticons when they were used to stand in for the Autobot resistance chiefs being addressed by Emirate Xaaron.
Optimus Prime had a Facsimile Construct of himself created by Wheeljack as a way of faking his own death so that he could test the Autobots' ability to survive without him. In this case the level of detail attached to the construct was such that the Autobots including Wheeljack were deceived into believing that Prime had in fact been killed.
When the Mayhem Attack Squad was training new recruits, they were pitted against several facsimiles in a live fire battle simulation.
Finally, a brainwashed Megatron was pitted against a facsimile construct of his future self, Galvatron for training, as part of the then-current Decepticon leader Shockwave's plan to remove Galvatron's considerable threat to his leadership of the Decepticons.
IDW comics continuity
A considerably more advanced form of the technology, facsimile avatars, was employed by Decepticon infiltration units. Described as "bio-technological organisms grown in fusion tubes", they were synthetic human mimics, created from cell samples culled from real humans that the Decepticons kidnapped to act as templates. Once activated, facsimiles could look, think and act entirely like the human they were spawned from. In fact, the Decepticons often planted long-term facsimiles back into civilization, and they lived normal lives until their dormant programming was activated or they are recalled. While totally obedient to their Decepticon masters, the facsimiles still possessed some form of innate creativity and even curiosity.
Additionally, all facsimiles grown in the same fusion tube "batch" apparently shared the same cellular template. As a result, the Autobots expressed an interest in capturing a Decepticon facsimile "alive", and using it as the key to access all other Earthbound facsimiles, and then either locate them all or shut them all down.