The "Sensitive" check box is available when creating a note within a record (1).
The purpose of the check box is indicate to users that the note contains sensitive information. A note that is marked as being sensitive will display highlighted in red (2).
Sensitive notes are viewable to users, there is no current permission that restricts a user from viewing sensitive notes. The red highlight is used as an indicator only.
To change a users permission regarding notes, please refer to the following knowledge base article Why can't I see a particular document/tab/branch/record?.