Vibranium is a rare metallic element from the Marvel universe. In Marvel's Captain America: The First Avenger, it is the metal from which Captain America's shield is made. The shield constitutes the entirety of the known supply of vibranium on Earth in the 1940s.
Vibranium is said to be able to absorb most kinds of energy in massive amounts. Consequently, it is virtually impossible to damage. In practice, events in Marvel's The Avengers indicate that it actually reflects energy above an unspecified threshold, resulting in a massive shockwave when it was struck by Thor's hammer. The energy absorption was sufficient for Captain America to fall several stories from a building onto a concrete sidewalk without suffering significant injury by landing on his shield.
Vibranium has unspecified properties in common with palladium that make it useful in the construction of an arc reactor. Vibranium is actually superior in whatever role the materials play, as palladium decays over time and escapes from the reactor, while vibranium remains stable.
Tony Stark developed a process to synthesize small quantities of vibranium, but the scalability of the process is unknown.