The computer control system that actually operates a building's mechanical and electrical equipment day to day - HVAC, lighting, access control, sometimes fire and security systems - monitoring sensors and adjusting equipment automatically to keep the building running efficiently. Also called a BAS (Building Automation System) in some regions.
The BMS is where a building's 7D and AIM data becomes genuinely operational: equipment tags and system data captured in the model during design and handed over through COBie are exactly what a BMS needs configured correctly to actually control the right piece of equipment - a poorly handed-over model means a facilities team reprogramming and relabeling everything manually after move-in.