Hi Ann. Dan from Trulia here.
I assume you're referring to the "Unclaim listing" text that appears on the My Listing page for a listing that you have branded using Brand Your Listings. (More here for people who are curious -- http://www.trulia.com/agents/brand_your_listings/
By branding the listing to begin with, you've gotten a number of benefits:
1. Your name and photo on the listing.
2. This listing and its stats on your "My Listings" page.
3. This listing and any others you have branded show on your public profile page.
4. You get a weekly email with stats on this listing aggregated with any other listings you've branded.
If you "unclaim" the listing, these all go away. Unclaiming, however, would be the appropriate thing to do if you are no longer the listing agent for that listing, or it is no longer on the market.