Short answers, pulled from the story.
Helios is the ancient Greek god who personifies the Sun. He was the son of the Titans Hyperion and Theia, brother of Selene, goddess of the Moon, and Eos, goddess of the Dawn. Though relatively minor in Classical Greek religion, he was the patron god and founding ancestor of the island of Rhodes, where he was worshipped more prominently than anywhere else in the ancient Greek world.
Phaethon was a son of Helios who asked to drive his father's sun chariot for a single day. Helios swore by the river Styx to grant the request, despite warning Phaethon of the dangers. Phaethon lost control, the earth burned and froze in turn, and Zeus struck him with a thunderbolt. His sisters the Heliades wept at the river Eridanus and were transformed into black poplar trees that shed tears of amber.
The Colossus of Rhodes was a gigantic bronze statue of Helios built at the port of the city of Rhodes by Chares of Lindos. It stood approximately 70 cubits, or 33 meters, tall and was counted among the Seven Wonders of the Ancient World. An earthquake in 226 BC brought it down, breaking it at the knees, and an oracle forbade the Rhodians from rebuilding it.
Helios was frequently invoked as a divine witness to oaths and treaties because his all-seeing nature made him a reliable guarantor of sworn words. He was one of three gods named to witness the truce between Greeks and Trojans in the Iliad. The League of Corinth and treaties between Smyrna and Magnesia, and among Athens, Cetriporis, Lyppeus, and Grabus, all invoked his name.
In late antiquity Helios rose from a relatively minor deity to a central figure in Roman state religion. In 274 AD the Emperor Aurelian instituted an official state cult to Sol Invictus, identified with Helios under the title Helios Megistos. A century later the Emperor Julian combined Mithraism and Neoplatonism to produce a theology centered on Helios that scholars have described as practically monotheistic.
Odysseus's crew killed and ate Helios's sacred cattle on the island of Thrinacia, despite prior warnings. Helios's daughters Phaethusa and Lampetia reported the crime to their father, who demanded punishment from Zeus and rejected the crew's offer to build a new temple in Ithaca. Zeus destroyed the ship with a thunderbolt, killing every man except Odysseus, who had refused to touch the cattle.