I randomly encountered this address on blockchain.info: https://blockchain.info/address/1CzpppydnGN5dQN7iBnZbmm5RXreu7hrHW and at the top a message appears presumably describing the owner of the address. I have not seen this before. Is this just a feature of blockchain.info or is it a feature generally available in the Bitcoin system? And if so, how does this feature work?
This is known as "tags", and it is 'blockchain.info' specific. You can use any web page, or bitcointalk.org user profile or bitcoin-otc Id as link. Your link page should contain your address.
This is a feature of blockchain.info only, because it is stored in their database. It is possible for anyone to associate a link ("tag") with any bitcoin address on blockchain.info, as long as it can be verified that the page the tag links to also contains the same bitcoin address.
However, the example address provided in the question contains both a link and a short message. This happens for tags that point to user profiles on bitcointalk.org. The message displayed is simply the user signature from that forum.