Definitions for "Expediting"
Facilitating and accelerating progress by the removal of obstacles. Editor's Note: This is an important part of a project manager's job, especially in Procurement Management. [D02742] Webster
Determining where an in-transit shipment is and attempting to speed up its delivery.
The 'rushing' or 'chasing' of production or purchase orders which are needed in less than the normal lead time.
Customers will many times call to move up their ship dates and it’s called expediting. Sometimes there are additional costs (overtime, material shipping charges etc.) to do this for them. Those are called expediting charges.