Adamantite Ore is a type of ore that can be obtained once hardmode is activated in a world and at least three Demon/Crimson Altars have been destroyed. Once the preceding conditions have been fulfilled, either this ore or Titanium Ore will spawn in the world.
To mine the ore, a Mythril Drill or better is needed. Adamantite Ore, like all hardmode ores, cannot be broken with Explosives.
Because Adamantite Ore will only spawn at or below the depth that lava starts appearing at, the top of the Underworld is generally a good place to find relatively large quantities of it.