Priority shipping is used when deciding to load a vehicle.
First, all priority items are loaded. Then, if any space is left the oldest non-priority items are loaded, and so on until the vehicle is full.
It doesn't mean that the item WILL go next day - you'd need Guaranteed Delivery for that.
And "How long" depends on where it is coming from, where it is going to, whether it is airmail, and whether you are in a rural or urban area.
Most delivery companies have a time calculator on-line.
2-3 days, usually