To protect your privacy, you should select this option if you using myPhoneDesktop Web Client on a public computer (i.e., Internet Cafe, Local Library, Hotel, Airport Kiosk, etc.) or using your friend's computer. The "Public or Shared Computer" option is selected by default. Uncheck this option only if you are the sole operator of the computer and you are certain that the computer you are working from is "safe" (i.e., personal computers in your office or home).
Be sure to log off via "Settings | Account | Logout" when you have finished using myPhoneDesktop Web Client and close web browser to end your session.