When USPS tracking information says PROCESSED THROUGH USPS FACILITY it means that your package has arrived at a USPS sorting facility and has gone through the processing and has then been loaded onto a truck to be delivered to your local post office or to another USPS sorting facility.
Sometimes packages can go through as many as 3 to 4 USPS sorting facilities depending on the destination of the package.
When a package is mailed out to someone the package goes to a local post office and then to another sorting facility in another town.
Then the package gets sorted and loaded onto another truck which is a semi with a large trailer with thousands of packages.
Then the USPS semi truck arrives at another sorting facility on it's route and then the sorting facility employees unload the packages and then sort them again.
Then your package goes onto another truck which then takes it to another sorting facility where it's sorted and processed again.
Then it may go to your local post office.