What is this fixture on my external water faucet and how can I remove it?
Backflow preventer:      The fitting closest to the faucet MUST unscrew CCW. 

Looking at your bib at the house siding, its not secured.  Use a second wrench on the faucet, torquing in the opposite direction to the wrench on the backflow adapter.  This will prevent you from busting the water pipe and REALLY making a mess.  Backflow article