Mohair is one of those textiles where the name gives you absolutely no hint about what it actually is. It isn't like there is a "mo"-creature running around that you can point at and say "hey, that thing makes mohair!" The only hint from the name is that it is some kind of hair, and hopefully not from your cousin Mo.
What it actually is happens to be hair from an angora goat. Keep in mind that this is not the same creature that makes what we call angora--angora comes from a rabbit. Why is an angora goat not called a mohair goat? Your guess is as good as mine. The history of the goat is kinda murky, probably because as history has rolled along there have been more interesting things to document than the domestication of particular goat species. But, it seems to be a variety of Asian goat that Turkic tribes have traditionally raised, based on the regions and dates several websites have cited in their histories of this particular type of goat. What makes it different from the cashmere goat is that the cashmere goat has two different layers of hair, with the underlayer being cashmere, whereas with the mohair goat only grows one layer of hair and that is mohair. Also, to get the best hair from an angora goat it is shorn whereas a cashmere goat is combed. The best mohair comes from younger goats (think cute, fluffy baby goat!). Mohair is considered a sustainable fiber because goat hair is an easily renewable resource and can be done using sustainable farming methods.
this Missoni cardigan. The lower quality mohair is used for things like carpets and industrial uses. The grading of quality has to do with the thickness of the individual hairs, with the thinner the hair the higher the quality. So, that mohair sweater that you've been rocking all winter is actually made of goat hair!
Top picture from Angora Goat and the sweater is from Bluefly, other information from wikipedia and personal experience.