Cotton is a cellulose fibre of vegetable origin. It has a fairly long staple and can thus be spun into very fine thread. It is hard-wearing and takes colour well. However it was not grown in Europe in period, but was imported from the Middle East: The fibres of cotton itself are shorter than linen, making it a poor choice for a warp.
"Arab merchants brought cotton cloth to Europe about 800 A.D.. When Columbus discovered America in 1492, he found cotton growing in the Bahama Islands. By 1500, cotton was known generally throughout the world".
The word cotton may have originally referred to a weave rather than a fibre. The word "Fustian" has been around since the 12th century (England) and refers to "a hard-wearing fabric of cotton mixed with flax or wool with a slight nap" although it appears to have originally referred to a linen and wool cloth.