Adamantium is a fictional alloy of Marvel Comics, known most famously for being the substance that makes up the outer metal layer of Wolverine's claws and skeleton. The compound is essentially indestructible (there have been some of those rare, "only in a comic book" moments) and thus its a pretty great thing to have on hand if you want to survive a fight / gunshot / thermonuclear war, etc.
It was invented in the 1960s by a scientist, Dr. Myron MacLain, looking to replicate his previous success Vibranium (another fictional alloy) of Captain America's shield. Its chemical components are a closely guarded secret, and poorly crafted adamantium is no better than any other metal, so its supply is extremely limited.
Besides Wolverine, adamantium can also be found on the following Marvel characters: Sabretooth, Lady Deathstrike, X-23, Cyber, Bullseye, Doctor Octopus (a special set of his arms), and its first owner, the archvillain robot Ultron.