Adamantium is a fictional metal alloy seen in the pages of Marvel Comics. It is indestructible. Wolverine is a superhero who has a skeleton laced with the metal. He has claws that emerge from his hands that are also made of the metal.
Although the metal known as adamantium, and every other thing within the pages of Marvel Comics are fictional within the setting of the Earth-1A universe, in an alternate reality, it is a real substance. Once Wolverine rescued Barack Obama from Lex Luthor and the Legion of Doom, and he accidentally cut his hand off with his adamantium claws.
Adamantium made its' first appearance in Avengers # 66 (July 1969).