Busiris is the Greek name of a place in Egypt, which in Egyptian, was named djed (also spelt djedu). The location was a centre for the cult of Osiris, thus the reason for the Greeks choosing the name. The word Busiris was also used to refer to chief god of Busiris, an attribute of Osiris.
In Greek mythology, Isocrates, in his witty declamation Busiris recounts "the false tale of Heracles and Busiris" (11.30–11.40), which was a comic subject represented almost entirely in the repertory of early 5th century BC Athenian vase-painters: the theme has a narrow narrative range, according to Niall Livingstone: Heracles being led to sacrifice; his escape; the killing of Busiris; the rout of his entourage.
The brief synopses concerning Busiris in pseudo-Apollodorus' Bibliotheke are at II.1.5 and II.5.11: Busiris there is one of the fifty sons of Aegyptus, betrothed to a Danaid. In Isocrates' rhetorical use of a theme that he considers unworthy of serious treatment, the villainous king of Egypt named Busiris, a son of Poseidon and Anippe, daughter of the river-god Nilus, was the ancient founder of Egyptian civilization, with an imagined "model constitution" that Isocrates sets up as a parodic contrast to the Republic by Plato. The monstrous Busiris sacrificed all visitors to his gods. Heracles defied him, broke his shackles at the last minute and killed Busiris.
In Didorus Siculus, Busiris appears as the founder of the line of kings at Thebes, an apparent description of the originator of the Eleventh Dynasty, and likely an analogy to Amun. As Didorus confuses Osiris with another figure in his stories of Nysas and Dionysius, and this figure may be Belus, or Baal, who was equated with Montu, another deity of Thebes, his confusion of Busiris, Osiris and Amun may be a clue to unraveling the confused Greek tradition around the name.
This part of the mythology concerning Herakles appears to have origins in a corruption of an Egyptian myth concerning Osiris' sacrifice by Set, and subsequent resurrection (see Legend of Osiris and Isis).
The fictional king Busiris also appears, as the leader of a revolt, in the ironically-titled True History (2.23) by Lucian, written in the 2nd century CE.
In Paradise Lost, John Milton uses "Busiris" as the name of the Pharaoh of the Exodus, which suggests a comparison between Heracles' escape and the Israelites' escape from slavery.