Nothing. They won't even know. Federal law protects the privacy of your medical records. No one will know about your treatment unless you inform them. You cannot be discriminated against because you receive treatment for depression. Most employers and schools would prefer that their students and employees receive treatment so that they can be successful.
Only you can answer this. If you are experiencing depression, the chances are that someone else in your family may have already experienced this problem, too. Your parents and brothers and sisters may have already noticed changes in your behavior and are concerned about you. They may be relieved that you are getting help.