Noodling is the practice of catching catfish by letting them latch onto your arm.
To begin, a noodler goes underwater to depths ranging from only a few feet to up to twenty feet, placing his hand inside a discovered catfish hole. If all goes as planned, the catfish will swim forward and latch onto the fisherman's hand, usually as a defensive maneuver in order to try to escape the hole. If the fish is particularly large, the noodler can hook the head around its gills.
This video captures some noodling fishermen in action.
(via that's how it happened)
Update: There's a documentary on noodling called Okie Noodling. (thx to many)