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 only viewable to users with "View Sensitive Notes" role. 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?.