A mothers room, or lactation room, is a private space for nursing mothers to express milk during the working day. In the US the PUMP Act requires most employers to provide one (a bathroom does not count); UK and Australian guidance points the same way. Requirements typically include privacy, a power outlet, a comfortable chair and nearby refrigeration.
Operationally the room must be genuinely available when needed, which is why booking beats first-come: a mother should be able to reserve her slots for the week, privately, without negotiating at the door. Privacy settings matter; who booked the room should not be broadcast on a public panel.