Kemp refers to the coarser hairs in the fiber. Down hairs are fine, Kemp is very very coarse. They usually take up dye differently from the down fibers as well.
(posted by me this day on spin-list)
Usually kemp is removed from the fiber in processing. If it is in raw fleece, you can remove it with combing. In cashmere, it is usually hand-plucked from the down so as not to lose any of the down. In medium wools such as Jacob and coarse wools such as Navajo Churro, it may be left in.