What is the purpose of these ducts in HVAC/laundry room ceiling?
Make-up air
Vented clothes dryers and bath fans exhaust air to the outside.  Something has to provide a replacement for that air, and in old buildings, that was done by simple leakage of outside air into the structure.  However, that means we can't control anything about the outside air that gets in, which is an issue from an energy-efficiency (heat/cold) and building-performance (humidity/moisture) standpoint.  It also means that they can depressurize a building, which can send things like combustion exhaust gasses flowing the wrong way, with the attendant CO hazards that poses.
So, modern buildings seal up the leaks and cracks and then bring make-up air in explicitly when and where needed.  This provides the opportunity to direct make-up air supply to where it's needed, damper it off if it's not needed at a given time, or precondition it (such as in a heat-recovery or energy-recovery ventilator) before it gets dumped into the room in question, improving energy efficiency and humidity control.  It also means that the supply of combustion air for appliances is brought in explicitly, guaranteeing its presence vs. relying on random leaks to get the job done.