A strand of cloth fiber

strand: A single thin length of something such as thread, fiber, or wire, especially as twisted together with others

http://www.oxforddictionaries.com/us/definition/american_english/strand

Right. But I was more interested in the other part of the phrase which is "cloth fiber". I tried googling it, but it seems like it doesn't really mean anything that makes sense. I'm curious, maybe "a strand from a cloth" would mean a single piece of thread taken from a cloth?

Thanks!

MustAskRight. But I was more interested in the other part of the phrase which is "cloth fiber"

Fibre that came from a cloth or could be used for making cloth.