Azazel is Kurt's biological father. he has the same physical characteristics as Kurt, but is red. He also has the power of teleportation, just like Kurt.
His first appearacne in the comics was Uncanny X-Men #428, where he was introduced to Mystique by her husband, Christian Wagner. Herr Azazel was stated to be ruler of an island nation off the coast of Bermuda, La Isla des Demonas. The Island of Demons, where Havok's teacher had discovered traces of an ancient mutant civilization in Uncanny #422. for all appearances, he seemed to be a suave and charming nobleman, and he managed to seduce Mystique with his charm. It was later revealed that he had the apeparance of a demon, with red skin, glowing yellow eyes and pronged tail.
in Uncanny X-Men 429, he was shown at the head of a demonic army, exiting a gate summoned by Kurt and his half brothers at the end of the issue.
According to old religious texts, Azazel is one of the chiefs of the 200 fallen angels. The name 'Azazel' may be derived from 'azaz' and 'el' meaning 'strong one of God.' It is thought that Azazel may have been derived from the Canaanite god, 'Asiz, who caused the sun to burn strongly. It has also been theorized that he has been influenced by the Egyptian god, Seth. Azazel in Christian and Jewish theology is the demon the 'scapegoat' of the Israelites. The Lord ordered his high priest, Aaron, to 'place lots upon the two goats, one marked for the Lord and the other marked for Azazel' on the Jewish Day of Atonement. The goat designated by lot for the Lord is to be used as a sin offering, while the goat designated for Azazel "shall be left standing alive before the Lord, to make expiation with it and to send it off to the wilderness for Azazel." (Lev 16:10) Most importantly, Azazel was described as the leader of the 'Watchers' (biblical Watchers, not Marvel) who educated humankind in arts that led them to sin. He introduced men to weapons, causing violence in mankind, and women to cosmetics, which encouraged deception, and enabled them to seduce angels. The angels who were on earth with Azazel, coupled with the mortal women, producing the Giants, who were described to have animal heads and other such weirdness as offspring... when God learned of this, he had the archangel Raphael bind him hand and foot and cast him into a pit where he was to remain until the day of judgement. The story goes: "the whole earth has been corrupted by [Asa'el's] teachings of his (own) actions; and write upon him all sin." . It was because of Asa'el's teachings that God sent the Flood to destroy the evil in the world including even the souls of the giants, so that all evil will be wiped away from the face of the earth.
"And Azazel taught the people (the art of) making swords and knives, and shields, and breastplates; and he showed to their chosen ones bracelets, decorations, (shadowing of the eye) with antimony, ornamentation, the beautifying of the eyelids, all kinds of precious stones, and all coloring tinctures and alchemy." - 1 (Enoch 8:1)
Azazel is also referred to as Iblis, or Eblis, a djiin or demon of Islamic lore whose name means 'Despair'. According to the legend, when God commanded the angels to worship Adam, Azazel refused, contending (in the Koran) "Why should a son of fire fall down before a son of clay?" Whereupon God cast Azazel out of Heaven and changed his name to Eblis. Eblis is the equivalent of the Christian Satan.
Whether any of these stories relate to the character currently appearing is unrevealed.