Both pages and spaces can be secured.  Space security is controlled by a wiki admin, page security can be controlled by the author.  Page "view" security is inherited by child pages, "edit" is not.  So, if you only allow yourself to view Page A, and Page B is a child of A, only you will be able to view Page B.  Additionally, the ability to edit is restricted by the ability to view.  So, if someone doesn't have permission to view, they can't edit either.  You can read more in the confluence security documentation.