Private Posts are totally private.  Only *YOU* can read them, and only when you are signed in.

To make a post "private", you need to be signed in and on your private home page:

http://www.xanga.com/Private/home.aspx

A Public Post will be have a link under it that says "PUBLIC". Clicking on this link for a particular entry will make that entry private. It will no longer appear on the public version of your Xanga site, which you can verify by clicking the PUBLIC PREVIEW page on the top of your private home page.

If the newly private posts still appears on your public site, it may be related to the following issue:

When I visit my Xanga site, the latest updates don't show up?!
http://help.xanga.com/aggressivecache.htm