The make item private option only exists in three areas - Tasks, Tickets, and Calendar. It is used when you need to assign a task or ticket to a contact(s) or keep a calendar event private and want to only allow those contacts to view it. If you submit the task without checking the private box, then all contacts will be able to see that task and who it's assigned to. If you check the make private box, then only you and the 2 contacts assigned to it will be able to see the task and get notified that it was created. It is therefore hidden from the rest of the contacts associated with the project. You can mark items private when adding them by checking mark private at the bottom of the Add Responsibility box.
This does not apply to other sections, such as conversations, because you do not assign a conversation to someone. With a conversation, you simply indicate which contacts should have permission to view and take part in the conversations. In that case, the conversation is hidden from those who are not given privileges to take part in it. Therefore there is no need to mark a conversation private separately, per say.