Clicking 'unpublish' puts a "sitter found" message at the top of the ad and removes it from the list of available sitting positions so it's no longer in the search results. It also removes the contact message box from the bottom (so you can no longer be contacted from the ad page).
The ad isn't totally removed for a number of reasons. If we did remove all unpublished ads from the site there would be hundreds of '404 not found' error pages on the website. Also sitters still have notification emails in their mailboxes with links to the page. By keeping the page and adding the sitter found message, if they click the link to it, they will see that the position is no longer available and wont contact us asking why there is an error page.
If there is something on the page you no longer want anyone to see you can always change the text on the page.