Visibility for Coaches/Mentors means whether Coachees/Mentees can see you in their list in order to pick you for Coaching/Mentoring and/or for sending you a Connection Request.
It gives you the flexibility so that if you do not have the capacity to support etc, you are not approached. Coachees/Mentees can also change their visibility.
Your visibility is set within your Profile.
Click on 'Settings', then 'Edit My Profile', select the 'Contact details' tab and under 'Visibility' select the appropriate setting from the drop-down menu.
e.g. 'Visible to all Users from all Organisations', 'Visible to Users only from my Organisation' or 'Hidden from all Users (except Administrators)'.