When a package has been processed at USPS facility it means that the package has been sorted through the USPS sorting facility and has been put onto a truck for delivery to either your local post office or to another USPS sorting facility.
The USPS facility is a sorting facility where thousands of packages are sorted daily and then put on a semi truck for travel to it's next facility or local post office.
Some USPS packages go through more than one sorting facility before it reaches your local post office.
When someone sends a package to you it goes to their local post office, then goes to a sorting facility where the package is again sent to another sorting facility and then once it gets to your state the package goes through another sorting facility where the package is then put onto a truck for delivery to your address.
Or if you get your mail at your local post office then the package will be held at the post office and say available for pickup.
When your package tracking on USPS says out for delivery or available for pickup then it means it's arrived at your local post office.