The VIDEO button is one of the buttons that selects the input going into the projector. 

When the VIDEO button is selected the video input socket on the desktop is connected to the projector video input.

Also, the projector input is changed form vga to video.

Also, the auxillary audio input sockets on the desktop are connected to the room's wall mounted speakers.

The button panel controls the AV switcher in the desk rack.  The VIDEO input can be selected using the AV switcher if the local button panel is not working.