"This Browser" is a sink that allows for playback within the browser you are currently using as an interface. This is useful if acacia.plethra.com is accessed from a machine that doesn't have the back-end service installed, but at least one back-end service is installed somewhere on the network (excluding mobile devices).
"This Browser" sink is only accessible from that window on that particular machine, making it the only "private" sink available.
Note - on Windows, Bonjour must be installed (if the back-end service is not) in order for acacia.plethra.com to function. Bonjour is automatically installed with iTunes.