On a Federation starship, the plasma relay room was an area where electro-plasma from the MARA of the warp core could be routed to different areas and systems of the vessel to increase or decrease power to these areas and systems as necessary. In short, it was an area used to control power transfers.
Aboard an Intrepid-class starship, the plasma relay room was found on the lowest deck of the vessel, Deck 15. It was manned by a single crewmember, usually a crewman. Power transfer requisitions were brought to this crewman on a PADD. The crewman then made the necessary transfers as per the requisition.