According to legend (and Hercules), King Phrixis sacrificed to Zeus the skin of a ram that was made of pure gold and imbued with the power to heal any illness. Legend has it that the fleece hangs in a pagoda on the island of Korsenia, and doom awaits all those foolish enough to try and take it.
In order to save King Aeson from a mysterious illness, Jason and the Argonauts set sail for Korsenia. They survive the Siren and make it to the island, and defeat Ares's giant Talos who stands guard over the pagoda housing the fleece.
Jason and the surviving Argonauts bring the fleece back to Corinth and heal King Aeson of his illness. Ares then snaps King Aeson's neck and stabs Jason in the chest, and after a fight between Ares and Hercules, the fleece is used to heal Jason.
The fleece is not mentioned during the season 1 episodes, but the fleece presumably remains in Jason's possession. It appears again in the book Cheiron's Warriors:
Jason shook his head. Being reasonable was getting him nowhere, so he moved over to the throne. Stepping up to it, he glanced at the golden fleece that hung above and behind it. He had led Hercules, Iolaus, and the others to get the fleece in order to save his father's life. His father had still died in the end, killed by Ares. But the fleece was Jason's. He swore he would never let it leave Corinth's throne room for as long as he lived.
Jason seated himself on the throne. As Ophistus always insisted, he sat up as straight as his spine would allow. He rested his hands on the throne's flared armrests.
- Excerpt from "Cheiron's Warriors".
"Maybe I don't understand centaur ways as much as I thought. But I do understand this: Corinth has a strong army. We've successfully defended out borders for decades. You know how you said the people of Corinth are prejudiced against your kind? Well, those same people will see you invade and believe all the lies they've heard about centaurs being subhuman. They will rally behind the army."
Jason leaned forward. "And I have the golden fleece. Against a powerful giant and the god of war himself, I won the fleece. I think it will take more than even the mighty Centaur Nation to take it away from me."
Golden Fleece from HtLJ "2.14 - Once A Hero"
The fleece is seen again in the HtLJ episode "2.14 - Once A Hero", when the Argonauts gather together for a reunion. Iolaus remarks that it's been ten years since they brought it back.