Short answers, pulled from the story.
A Greek hero cult was a form of worship directed at a dead man venerated at his tomb or a designated shrine because his fame in life or unusual manner of death gave him power to support and protect the living. Rituals were chthonic in nature, involving libations poured in the dark hours and sacrifices not shared by the living, since heroes were believed to dwell beneath the earth rather than on Mount Olympus.
Greek hero cults were chthonic, directed downward toward the earth, and their rituals more closely resembled those for Hecate and Persephone than for Zeus and Apollo. Heroes were thought to remain beneath the earth after death and retained purely local power, unlike the Olympian gods whose influence was universal. The distinction between hero and god was not always certain, particularly in the cases of Heracles and Asclepius, who could be honored as either.
After the Battle of Marathon in 490 BC, the 192 Athenian dead were buried on the battlefield beneath a mound that became known as the Marathon Tumuli. Chthonic cult was dedicated to these fallen soldiers, as offering trenches at the site indicate. Whitley interpreted this as the city-state co-opting hero cult as a political gesture in the archaic tradition.
According to Herodotus, the Spartans believed that possessing the bones of Orestes would transfer his heroic power and protection to Sparta, enabling their conquest of Arcadia. The theft of the bones from the Arcadian town of Tegea was credited by the Spartans with securing that victory. This reflects the belief that a hero's physical remains carried his local protective power.
Whitley distinguished four or five types: oikist cults honoring colonial founders at their graves; cults to named heroes from the Iliad and the Epic Cycle; cults to purely local heroes not found in Panhellenic epic; cults established at Bronze Age tombs identified archaeologically by Iron Age deposits; and oracular hero cults where an oracle developed around a figure, as in the case of Amphiaraus.
Sparta deliberately cultivated hero cults as political propaganda, recognizing that the population responded to these shrines in politically useful ways. When Cleisthenes reorganized Athens into new voting demes, he consulted the oracle at Delphi on which heroes should lend their names to each division. The veneration of the Marathon dead under a state-built tumulus also represented the Athenian city-state transforming battlefield sacrifice into civic cult.