It refers to shipping a package on priority request of the customer.
Expedited shipping refers to fast shipping. It is a process of shipping a parcel at faster speeds than usual. There is no exact definition of how fast will these services be, but usually depends on the terms and preference of the shipper.
Expedited shipping can vary anywhere between same day delivery to 3 days. It is also more costly than regular shipping since such parcels are marked separately and prioritized over the others.
Sometimes expedited shipping is also referred to as express shipping, however, the exact distinction or similarity depends from carrier to carrier. Offering expedited shipping options to customers helps in driving conversions, because customers want faster delivery options.