Short answers, pulled from the story.
Hyllus was a son of Heracles and Deianira, and the husband of Iole. Heracles charged him on his deathbed to marry Iole, and together they had a son named Cleodaeus and three daughters: Evaechme, Aristaechme, and Hyllis. Hyllus led the first attempt by the Heracleidae to reclaim the kingdoms Zeus had intended for Heracles.
Hyllus was killed in single combat by Echemus, the king of Tegea. He had marched his army across the isthmus of Corinth to attack Atreus, the ruler of Peloponnesus, when Echemus faced him one-on-one and defeated him before the larger battle could be decided.
The oracle told Hyllus to wait for 'the third fruit' and enter Peloponnesus through 'a narrow passage by sea.' Hyllus interpreted this as three years and the isthmus of Corinth, and was killed when he acted on that reading. Generations later, the oracle clarified that 'the third fruit' meant the third generation, and the narrow passage was the straits of Rhium, not the isthmus.
The three branches of the Dorian people took their names from Hyllus, Pamphylus, and Dymas. Pamphylus and Dymas were the sons of Aegimius, who adopted Hyllus and granted him a third of his territory. Herodotus recorded, in book five, a Dorian tradition holding that Hyllus was actually an Achaean by blood.
Hyllus and Iole had a son named Cleodaeus and three daughters: Evaechme, Aristaechme, and Hyllis. Cleodaeus later led the third attempt to reclaim Peloponnesus, following the earlier efforts by Hyllus and his brothers.
The Return of the Heracleidae was the successful conquest of Peloponnesus by Hyllus's descendants, completed generations after his own failed attempt. The victors divided the peninsula by lot: Argos went to Temenus, Lacedaemon to Procles and Eurysthenes, and Messene to Cresphontes. The Heracleidae held the throne of Lacedaemon until 221 BC.