Adamantium is a rare metal that is also indestructible and powerful. It is a cousin metal to vibranium.
Vision is carrying out his objective: acquire pure adamantium
Wolverine is also known to have adamantium bonded to him by Weapon X that makes him unbreakable and his claws sharper and stronger. Vision steals some of adamantium from a Weapon X facility in order for Ultron to construct himself a new chassis.