He was the eldest son of Priam and Hecuba, called "breaker of horses" though he never seems to do so. With his wife, Andromache, he fathered Astyanax. He had a horse named Lampos and friends named Misenus and Poludamas. His charioteer was Cebriones, his half-brother.
Hector provides a stark contrast for Achilles, who was from first to last a man of war. Hector was fighting, not for personal glory, but in defense of his homeland. His words, "Fight for your country - that is the first and only omen" became a proverb to patriotic Greeks. Through him we can see glimpses of what life might have been like in more peaceful times. The scene where he bid a final fairwell to his wife Andromache and his infant son is one of the more moving scenes in the Iliad.
During the Trojan War, Hector killed Protesilaus and was wounded by Ajax. In the portion of the war described in the Iliad, he fights with many of the Greek warriors and usually (but not always) succeeds in killing or wounding his opponent.
Nonetheless, Hector's fate is never in doubt. Achilles, raging over the death of Patroclus, kills him and drags his body around the walls of Troy. Ultimately, with the assistance of the god Hermes, Priam convinces Achilles to permit him to bury Hector. The final passage in the Iliad is his funeral, after which the doom of Troy is just a matter of time. In the final sack of Troy, as described in Book II of the Aeneid, his father and many of his brothers are killed, his son is hurled from the walls in fear that he would avenge Hector, and his wife is carried off by Neoptolemus.