Currently in use for Diablo III and the Mists of Pandaria beta is the "Battle.net Update Agent" program or "Agent" for short. This program is designed to make game launching and patching more efficient, especially if you have multiple Blizzard titles running on your computer.
Agent must be allowed to run in order for you to play our titles which utilize it, so please ensure that any security software you have on your computer is not mistakingly blocking the Battle.net Update Agent.
As it currently operates, Agent should shut itself down around ten seconds after closing out all supported Blizzard games. If an Agent process remains running on your computer long after shutting down any supported titles and you need it to close, simply restart your computer. Alternatively, you can manually end the process in Windows Task Manager.