«why is there a statement showing last update after search at the page bottom? What is the significance and is it relevant? »
The search function on the
dmoz site runs off of an index which must be periodically regenerated. (I believe this happens about twice a week). Changes made to individual categories and site listings are generally immediately visible when browsing the directory, but will only show up in the search engine once a new index ("search database") has been created.
So if your site is added on 2/14, but the search database is from 2/13, it will not show up in a search. Once the database is generated after 2/14 (say, 2/17), the site will show up in a search.
It's mostly useful to editors and those submitting sites; who are the primary users of the
dmoz.org site.
Note that some changes are being made to search at present, and it is coming up as unavailable; you can still see the last update note at the bottom of the results page, however.
-sam