Use DVD Player in Fullscreen Mode on an External Monitor
By default, DVD player will exit fullscreen mode when it’s not the active application. This is a problem if you want to watch a movie on an external monitor while working on a primary monitor. To get around it, go to Preferences in DVD Player (DVD Player -> Preferences… or command + ,), switch to the “Full Screen” tab, and ensure that “Remain in full screen when DVD Player is inactive” is checked. This should achieve the desired results.
Source: MacRumors.com Forums