I am wondering how to change the description of my stable so that it shows what kind of horses I specialize in breeding and selling. Also is it possible to board horses belonging to other players.

You can edit your "about this stable" at Stable>Stable Activities>Manage Stable Info/Bio!

For boarding other people's horses, I know some accounts do offer boarding services but it is not really a recommended thing to do - see this forum thread for an explanation (-click-)

Hope this helps!