If you are using the new version of the Web TeleConsole please follow this link to learn how to enable/disable public contacts.
When adding (or editing) a new personal contact in the TeleConsole, you will notice an option to toggle the status of a contact to be available for View (by) public.
Public in this sense refers to all the users on the phone system in your company. Once this is enabled, the contact will not only appear in your list of personal contacts but also in the personal contacts of every other user in the company. In other words, public contacts are shared by everyone in your company while non-public contacts are only available for you.