N.B. The screenshots and descriptions are for the iPhone/iPad version.

This is where you can add your own stables and remove yourself from stables you want to leave.
It displays a list of the stables you are currently a member of and whether you are the administrator of those stables. You can switch to different stables by tapping on the icon at the top left of the Home Screen.
On this page you can add new stables (which you would be an administrator of) or leave stables which you are a member of. You cannot leave stables you are the administrator of as you created the stables!
If you have removed yourself by mistake from particular stables, you will have to get a new 'Invitation Code' from the manager or administrator of those stables.
See also: Home Screen - Change Stables, User Screen - Add Stables.