When a package is being sent through USPS expedited shipping it means that the shipper or seller of the package is shipping the package through USPS using their premium or priority mail shipping so that the package is supposed to get to the person or business sooner than standard shipping.
Time sensitive packages or mail usually goes through USPS expedited shipping and the person or business shipping the package or mail pays more for the package to go through USPS expedited shipping.
Expediting means to send something faster than it normally would.
Still even with expedited shipping the package may still be delayed but usually the packages that are shipped through expedited shipping gets delivered much faster than standard shipping packages.