The Adamantium Arrow is a lethal shaft designed to fight Ultron, the robot made of the same unbreakable alloy. Adamantium is a very dense alloy that is virtually indestructible. A sufficient amount is capable of surviving multiple nuclear explosions with no damage.
While most Adamantium Arrows are standard broadheads, some are equipped with an electrical charge like the Electro Arrow. While Hawkeye sometimes refers to them as Adamantium Shafts, only the arrowhead is made of the priceless metal. Arrows require some amount of flexibility to fly properly, so a shaft made of inflexible adamantium would not work.
The Adamantium Arrow is a common trick for Hawkeye in the video games. It appears in Marvel Heroes, Marvel Avengers Alliance, and others.