Idling applications are programs that basically simulate idling in a server, so you can earn as many TF2 items as possible.
Well, not anymore. In the latest entry of the Official TF2 Blog, Valve's Erik Johnson explained that over the next few days they will start removing all TF2 items that were earned using external idling applications.
Meanwhile, everyone else who took the moral high road will soon be finding a new hat in their inventory. Kudos to you!