Address claiming allows you to link your name/nickname with your address on the Block Explorer. The claimed name will be displayed on the richlist.
Why should I claim my address?
There is no particular reason you should. Though in some altcoin communities it is highly respected if you do a name claim. This shows your support and long-term interest.
Important note:
You can only claim your address once. Name changes or removal requests only through the contact form. Inappropriate names will be removed.