Felt is a textile originally made from matted wool but today often formed from synthetic fibres. It is dense and insulating, yet soft and flexible, and unlike woven cloth can be cut at any angle without the edges unravelling and sewn into any shape.
Legends abound as to the origin of felt: the Chinese say that it was invented by a horseman who put wool under his saddle for padding, only to find that the sweat of the horse's body, and the friction of movement, had caused the wool to become a solid mass; in the Arab world, it was a camel. Europeans claim that a pilgrim used wool as a kind of insole for his sandals, while an Iranian story has it that Solomon's son was so inept at carpet-making that he wept bitter tears onto wool and stamped on it in fury; the end result in both cases was - felt. (If you've accidentally transformed your favourite woollen into felt, see How to unfelt a felted sweater for how to undo it.)
Apocrypha aside, felt has been known throughout Asia and Europe for thousands of years; the earliest illustration of felt is from a wall illustration painted in about 500BC in what is now Iran, and excavations in Siberian tombs from the same era have yielded felt artifacts. But it was probably discovered long before that.
The secret of felting lies in the structure of sheep's wool itself. Each naturally crimped fibre is covered with tiny scales coated with lanolin, an oil secreted by glands at the bottom of the hair follicles which functions to repel moisture and prevent matting. Once fleece is shorn from the sheep and washed in soapy water, the scales open and release their lanolin; if the resulting wool is agitated and sprinkled with water, the fibres become completely entangled, and voila! you have felt.
On the steppes of central Asia, where felt was probably discovered by shepherds, it remains a humble fabric used to make rough cloaks and shelters that provided warmth from the bitingly cold winds. Many tribal peoples continue to live in portable homes; where in warmer more southerly climes such dwellings are swathed in woven goat hair fabric that breathes yet repels rain, in harsher northern areas like Mongolia these structures - yurts or, more properly, ger - are formed from felt blankets laid over a pole and lattice frame. Rain that could cause the felt to rot is rare in Mongolia; snow is easily brushed off the structure, and the felt blocks the whistling winds and creates a cozy home. Felt mats insulate the feet from the cold ground, and dyed and embroidered felt tapestries brighten the walls of these circular portable dwellings.
Felt can also be used for rather more luxurious items. For example, beaver hats were for some centuries popular with the moneyed classes in Europe. Beaver felt is made from the downy under-fur of beaver pelts; this fur has a tubular covering that is more solid than the scales on sheep's wool but more difficult to process. Hat-makers used a solution of mercury and nitric acid to break down the fur, but their exposure to mercury caused many to become unbalanced: hence the term "mad as a hatter". Besides the toll it took on hatters, beaver felt almost decimated the European beaver population in the 14th through 16th centuries; one reason Canada was explored and colonized so aggressively by European trading companies in the 17th century was because of the abundance and quality of the beaver pelts that trappers were able to procure there.
Though beaver hats fell out of fashion, felt hats continue to be produced: the fez, the Stetson, the bowler, and many more are made of this versatile material. Felt is used in manufacturing, to polish metals and as washers, seals, and pads in machinery. It's remained a favourite of craft makers, and, as appliqued cut-outs, adorned the poodle skirts of the 1950s.
Thanks for many interesting details to "Felt's Storied Past" by Edward J. Keall, in Rotunda, the magazine of the Royal Ontario Museum