Yep, Paris' older brother. He killed Patroclus when the latter went out to fight in Achilleus' armor; Patroclus' death is what roused Achilleus to get off his ass and go fight. Achilleus killed Hektor and then, still enraged, cut holes in Hektor's heels and dragged the body behind his chariot around the walls of Troy. When Priam came to beg Achilleus for Hektor's body, Achilleus relented and convinced the Greek army to stand down for seven days to allow the Trojans to collect firewood for a pyre and prepare a proper funeral.
In general, Hektor was a bugbear for the Greeks; IIRC, he stopped Diomedes' rampage through the Trojan lines and led the charge that pushed Aias back to the Greek ships.
"You fought with Captain Reynolds in the war?"
"I fought with a lot of people in the war."
"And your husband?"
"I fight with him sometimes, too."