You can only farm Dark Iron Ore in two instances – Molten Core and Blackrock Depths. If you are a longtime player, it used to be mined outside of those instances, but the nodes were removed in the Shattering.
Also a new change in 6.0 – Dark Iron Ore nodes will respawn in Molten Core, even after clearing the instance.
There are many transmog items made from Black Iron Bars by blacksmiths, as well as some engineering items.
You can also farm the following materials: