Fulling or walking ("waulking" in Scotland) is a step in clothmaking which involves the cleansing of cloth (particularly wool) to get rid of oils, dirt, and other impurities. The word comes (possibly via Old French) from Latin fullo, a man who washed togas.

A fuller is the worker who does the job. In the process, fuller's earth was used. (This is a soft earthy material occurring in nature as an impure hydrous aluminium silicate.) The cloth might also be washed. After washing, to prevent shrinkage and wrinkling, the cloth would be stretched on great frames known as tenters and held onto those frames by tenterhooks. It is from this process that we derive the phrase being on tenterhooks as meaning to be held in suspense. The area where the tenters were erected was known as a tenterground.

In ancient times the process of fulling involved using the feet to wash the material in a vessel of stale human urine (a rich source of ammonia). Priests' urine was especially valued for this task. (One would hope that this was followed by a thorough washing.)

Originally, this was literally pounding the cloth with the fuller's feet, but from the medieval period it was often carried out in a water mill in which the cloth was beaten with wooden hammers, known as fulling stocks. Such mills were known as fulling mills.

On the other hand, tartans were woven from pre-dyed thread (thus we get the thread counts that form the pattern), so I'm not sure if the finished cloth was subjected to any sort of fulling or not. Possibly the thread was cleaned/treated before dyeing. It seems likely that fulling the cloth might cause the colors to bleed, which would not be desirable in tartan. Maybe Matt can explain further?