Abraxas is a being from Gnostic Basilides, though its exact origins seem to have been lost to antiquity. Some refer to it as the Great Archon, others as an Egyptian god and/or a demon, and there has even been some debate about Abraxas being a deity ranking even higher than the Christian God and devil, that combines all opposites into one being. However, it is uncertain as to the actual role and function(s) Abraxas served in the Basilidian system.
His appearance is said to be that of a hybridized, Chimera-like creature somewhat similar to a Basilisk or Chronos and known as an Anguipede. He is said to have the head of a rooster or lion, the body of a man, with legs replaced with serpents which in turn end in scorpions. In his right hand he grasps either a club or flail and he carries a rounded or oval shield in his left.
As an Archon
Irenaeus described a system where "the Unbegotten Father" is the progenitor of Nous (Mind). Nous then begat Logos, who begat Phronesis, who begat Sophia and Dynamis. This last pair produced the principalities, powers, and angels; the angels then create the first Heaven. They then serve as the progenitors of a second series, which ultimately create a second Heaven. This continues on and on until a grand total of 365 heavens exist - the angels of the last, or visible heaven, then create the planet Earth. The ruler of this entire set of 365 heavens is stated to be Abraxas.
It is stated that he rules as the great archon specifically because his name contains the number 365, which is the number of days in a year. This is a play on words however, as his name in these days was written as "ΑΒΡΑΣΑΞ": Α = 1, Β = 2, Ρ = 100, Α = 1, Σ = 200, Α = 1, and Ξ = 60.
As a Deity
As stated by Epiphanius, he is considered the power above all others, and the First Principle. It is mentioned that the Basilidians also considered the human body as possessing 365 parts (or mele), thus connecting him to the Earth even more strongly. It is stated that the entirety of the heavens was created in his honor, and also that Jesus the Christ was not sent by the Maker of the World ("God") but instead by Abraxas himself.
As an Aeon
Other accounts claim that Abraxus was an Aeon that dwelled with Sophia and the other Aeons of the Pleroma Dukias, within the light of the luminary Eleleth, who is said to be the last of luminaries (or spiritual lights) to have come forth. Aeon Sophia encounters darkness due to her association with Eleleth, and becomes involved in the Demiurge's ruling of Earth from which she attempts to make a salvage effort.
As such, the role of Aeons of Eleleth, including Abrasax, Sophia, and others, pertains to this outer border of the Pleroma that encounters the ignorance of the world of Lack and interacts to rectify the error of ignorance in the world of materiality.