This material is natural or synthetic material that is used for the body or thorax when dressing a fly. Dubbing is typically twisted around the thread and wrapped around the body of the fly. Modern materials like Nano Silk can be split and the dubbing can be trapped between the two split thread sections alternatively you could create a dubbing loop with a double wrap of thread, insert the dubbing use a dubbing twister to create a loop of dubbing. Obviously the more thread the thicker the body which is where modern materials like GSP's (Gel Spun Polyethylene materials) come into their own as they are extremely thing for their strength allowing fine layers of dubbing to be added to a fly with little thread build up.
What Can You Use for Dubbing A Fly?
Many materials are available, from coarse materials like hare's ear which is used as dubbing for the traditional GRHE (Gold RIbbed Hares Ear), Ice Dubbing which is an extruded synthetic sparkly yarn, traditional wools like Alpaca which in jumpers has lasted hundreds of years due to the think layer of lanolin which helps with floatability of flies through to Superfine Dubbings. If you want to go really superfine with dubbing then try mouse fur with Nano Silk, this makes incredibly fine fly bodies!