Kilayim, Chapter 9, Mishnah 3:
The Mishnah lists three types of cloths: "Mitpechos hayadayim, mitpechos hasefarim, mitpechos hasefag - ein bahen mishum kilayim" - hand cloths, book cloths and bath cloths are not subject to the prohibition of kilayim:
"Mitpechos hayadayim" - towels used for drying the hands.
"Mitpechos hasefarim" - the covers in which people would wrap and cover Torah scrolls and other books.
"Mitpechos hasefag" - towels used for bathing, that is, bath towels.
None of these are subject to the laws of kilayim, since they are not meant to serve as a garment.
"Rabbi Eliezer oser" - Rabbi Eliezer forbids them:
In Rabbi Eliezer's opinion these cloths are forbidden, since ultimately they are items that a person is likely to wrap around himself, and therefore they are subject to the prohibition of kilayim.
"U'mitpechos hasaparim asuros mishum kilayim" - and the barbers' cloths are forbidden because of kilayim:
Here the reference is to the cloths of the barbers - those cloths that were spread over a person during a haircut, in order to keep his clothes clean and to prevent the cut hair from falling on them. These cloths are forbidden because of kilayim even according to the first Tanna, because this is their normal manner of being worn: it is not something used merely for wiping, but something that a person actually wears, and therefore it carries the prohibition of shaatnez.
In summary: In this Mishnah we learned that hand cloths, book cloths and bath cloths are not forbidden because of kilayim, since they are not meant to serve as a garment, while Rabbi Eliezer forbids them because a person can wrap his body in them. The barbers' cloths, by contrast, are forbidden because of kilayim even according to the first Tanna, since that is their normal manner of being worn.