Does it go to the EGR valve?
That would be a vacuum line. They operate various devices so follow the line. Cars don’t like having vacuum leak and will stagger or stall depending.
Those are the vacuum supply lines for the HVAC system and cruise control.
If you remove the vacuum line from the engine and allow it to leak, the engine will speed up, the AIC valve will close to slow the engine to normal speed, then when you block off the air flow the engine will stall before the AIC valve can open.