USPS shipment acceptance means that the package was either picked up or dropped off at a USPS facility and the package has been accepted for shipping.
The package goes through an acceptance procedure first to ensure the package has proper postage and then when the package gets accepted it then gets sorted and put onto a truck where it's sent to a USPS sorting facility.
The USPS sorting facility is a huge warehouse like place where there are people working sorting packages and those sorting facilities are open 24 hours per day 7 days per week sorting packages and loading them onto the correct trucks to be delivered.
Your package then gets placed inside a large semi truck trailer where a semi truck driver comes and hooks up to the trailer at a certain time when the packages are loaded and then they deliver the packages and mail to another sorting facility or your local post office.
It's good news when your package has been accepted and means that your package is on it's way to you.
The package acceptance can take up to 24 hours but sometimes I've had packages stay on package pending acceptance for 2 days before.
USPS tracking is not very reliable and sometimes packages don't get scanned all the time like they should.