Mount Spy tells you what mount a player character is riding and how to get it. Simply click on a mounted player and Mount Spy will give you the details directly in your chat window. If the mount is from an achievement, the achievement is linked for your convenience. It will also tell you if you own that particular mount.
There's a fun and handy "Match Mount" feature: Just click on a mounted player then click "Match Mount", and if you have that mount it will put you on it.
If you don't want to see the mount information every time you select another player, uncheck the "Automatic Mode" checkbox. This switches the addon to only tell you the info when you click the "Mount Info" button.
If you have "Automatic Mode" checked, Mount Spy will continue to function even if its window is closed.
-- /mountspy getinfo : gets the mount info of your target
-- /mountspy hide : hides the MountSpy window
-- /mountspy show : shows the MountSpy window
Updated Nov 11 2018: The MountSpy window now stays hidden between sessions. This is an account-wide setting. You will no longer have to close the window every time you log in!