Nemeroth, a Chaos Space Marine psyker
Psykers are individuals with psychic abilities; the capacity to manipulate the Warp by strength of will. This is the equivalent of magic in the Warhammer 40,000 universe. The possible effects are numerous: offensive or defensive "spells", prescience, mind control, summoning daemons from the Warp, and so on. Generally the most powerful psykers come from the Eldar race (all of whom are psychic to at least a moderate degree), although Space Marine psykers – known as Librarians – from certain lineages may be equally powerful.
The Imperial Inquisition classifies psykers with a scale known as "the Assignment", which measures psychic reactivity within the Warp, and extends from Alpha-plus, representing a near-godlike level of psychic power, to Omega-minus, representing individuals so psychically null that psykers are mentally crippled in their presence. While most humans reside within the Rho-Pi range of the Assignment, representing no latent psychic power but with susceptibility to psychic stimuli, the Emperor himself represented an immense psychic power, explaining why his genetic children, the Space Marines, provide some of the most potent psykers known among humans.
A human Tainted Psyker
Due to the influence of the Ruinous Powers within the Warp, most psykers must undergo extensive training in order to defend themselves from the predations of daemons, malicious Warp entities spawned from excessive emotions. While all Eldar undergo such training as a matter of upbringing, many human psykers do not, and are trained only later in life by the Inquisition to become Sanctioned Psykers. Those who receive no such training are destroyed by the Inquisition, lest they fall to Chaos and become Tainted Psykers.
Space Marine Librarians who turn to Chaos willingly become Chaos Sorcerers, among the most powerful and dangerous psykers of all. Nemeroth is one such psyker.