Negative pressure means the duct system is put under continuous suction while it's cleaned. A high-powered vacuum connected to the ductwork pulls air — and the debris the technician agitates loose — out of the system and through a HEPA filter, which captures fine particles rather than recirculating them.
This is what makes source removal safe for your indoor air. Without negative pressure, agitating the ducts would just push dust, dander, and debris out of the registers and into the rooms. The vacuum keeps everything moving in one direction: out.
The vacuum can be truck-mounted (most powerful) or a large portable unit; either can do a proper job, but the HEPA filtration and enough airflow to hold negative pressure across the whole system are what matter. A 'truck-mounted equipment' claim alone is not a quality signal — ask about HEPA filtration and how they confirm the system stays under pressure.