The meeting room aboard Kirk's Enterprise, furnished with a long table and a three-sided viewer, where the senior officers hold conferences, hearings and briefings.
The briefing room is where the senior officers of the original USS Enterprise meet away from the bridge. It is a plain compartment with a long table, a computer terminal for the science officer and a three-sided viewing screen at the centre so that everyone seated can see the display.
It is used from the start of the series. In Where No Man Has Gone Before the officers gather there to argue over what should be done about Gary Mitchell, and in Space Seed Kirk holds the formal hearing there at which he drops the charges against Khan and his followers and offers them exile on Ceti Alpha V.
The room serves the same purpose as the observation lounge of the Enterprise-D and the briefing rooms of later ships, giving the captain a place to hear advice before a decision.