The phrase "rush shipping" means delivering something quickly or urgently. It is a service that allows you to receive your package faster than normal delivery options.
Sentences with «rush shipping»
Since I ordered it two days before I needed it, I had to pay for rush shipping. (renttherunway.com)
So go ahead and knock out the rest of your shopping before you'll have to pay rush shipping! (lavenueblog.com)
We do offer rush shipping on certificates though for additional fees. (comedydriving.com)