Refers to a barbershop, often a small or single-chair establishment. Similar to 理髪店, but 理髪室 can emphasize the room itself or a modest shop.
See also: 理髪店 (りはつてん)
There is a small barbershop near the station.
Compound of 理髪 (rihatsu, 'haircut, barbering') and 室 (shitsu, 'room').