It’s been so long since anyone has seen either a tenter, or the hooks on one, that the word and the idea behind it are now quite mysterious, but at one time, the phrase on tenterhooks would have evoked an image that was immediately understandable. Tenter hooks were L-shaped staples, much like a bent nail, placed at regular intervals on a rectangular wooden tenter frame. When cloth emerged wet from the fulling process it was stretched out on these hooks, preventing it from shrinking as it dried – hence the phrase ‘being on tenterhooks’.
It comes from one of the processes of making woolen cloth. After it had been woven, the cloth still contained oil and dirt from the fleece. It needed to be fulled and blocked, much like handknitters treat their finished garments today. After fulling, the cloth was stretched taut on frames, or tenters, and the tenter hooks were the metal hooks used to attach the cloth to the frame. At one time, it would have been common in manufacturing areas to see fields full of these frames (older English maps sometimes marked an area as a tenter-field). So it was not a huge leap of the imagination to think of somebody on tenterhooks as being in an state of anxious suspense, stretched like the cloth on the tenter. The tenters have gone, but the meaning has survived.
Tenter comes from the Latin tendere, to stretch, via a French intermediate. The word has been in the language since the fourteenth century, andon tenters soon after became a phrase meaning painful anxiety. The exact phrase on tenterhooks seems first to have been used by Tobias Smollett in Roderick Random in 1748.
(information from World Wide Words and Exeter City Council Time Trails.)