- "No! No! That's just a prototype."
"What's it made of?"
"Vibranium. It's stronger than steel and a third of the weight. It's completely vibration absorbent."
"How come it's not a standard issue?"
"That's the rarest metal on Earth. What you're holding there? That's all we've got."
- ―Howard Stark and Steve Rogers
Vibranium is a very rare element that was first discovered by researchers during the early 20th century. Vibranium is a nearly indestructible metal, which makes it highly sought after. Most notably, Captain America's Shield is made completely out of vibranium.
After successfully proving himself as a soldier in the battle field, Steve Rogers was taken to a U.S. Army facility. He entered Howard Stark's workshop where Stark presented him with different types of shields to adopt as his main weapon as Captain America. Rogers was intrigued by a silver, circular shield lying on a shelf. Stark informed him that it is lighter than aluminum and stronger than steel and nearly indestructible. He also added that the shield was all they had of the mineral. 
Vibranium is an extremely rare element that possesses unique attributes. In a pure mass, vibranium forms a solid metal that is stronger than steel, but only a third of the weight, as well as being completely vibration absorbent. This makes the material nearly indestructible, as any attempt to physically damage the material will be negated on a molecular level as mechanical/kinetic energy will be absorbed instead of breaking any bonds in its molecular matrix. In general, this means that vibranium can absorb a wide variety of physical impacts, including high-caliber bullets, without taking any damage or weakening. 
- In the Iron Man 2 novelization, the element created by Tony Stark to replace Palladium in the Arc Reactor is called Vibranium. The subsequent release of Captain America: The First Avenger retcons that information.