Tenugui in all simplicity, is just a piece of cloth. Since the Edo period, tenugui have been considered as a piece of fashion. From there it has since become an integral part of daily life. You may notice them in bath houses used as towels or decoration. Maybe in Kendo Studios when the students take off their helmets. And perhaps in the backyards when the gardener is at work. They can be worn as bandanas, or as scarves with numerous styles of tying.
More modern adaptions of the tenugui is using it to accent the daily life. You could use it to wrap a tissue box at home. Or use it as a table cloth for meals. It can also accompany you on the go when you use it to wrap a lunchbox. If you're attending a party, you can wrap a few bottles of wine! There is also using it for pets! I'm sure they can enjoy the tenugui's as much as we do.
Check here for some images of tenugui in action.