To full when used in reference to textiles is to cause the fibers in a piece of already constructed fabric to felt together. ''To felt'' is often used instead, but felting refers to loose fibers whereas fulling refers to something which was previously knitted, woven, etc.
Animal hair and wool generally felts/fulls best. It is done by shocking moist or wet strands with sharp temperature changes, agitation, and often acidity or caustic substances (sometimes in the form of soap, which Swap reminds me is not acidic in and of itself). This causes the scales on the strands to interlock, creating a dense mat. This can easily be done on purpose or by accident in a home washer/dryer.
Fulling is often done to make dense, shaped, waterproof garments, such as hats, slippers, mittens, and jackets.