The gallery is the control centre for a live broadcast environment. It's where the producer, director, vision mixer, production coordinator and the live supervisor sit and connects to all other aspects of the live shoot, e.g. cameramen, soundmen, VT trucks.
The gallery can be next to a studio if filming a live studio performance, or it can be housed in bespoke trucks anywhere in the world, e.g. Wimbledon tennis championships, Olympics.
On smaller shoots that require an "as live" filming environment, the gallery can be reduced to a set of monitors and talkback between the producer and the cameraman, e.g. an underwater shoot where the producer remains topside but needs to direct the camera and see the footage as it is recorded.