At least on the platforms in the UK, the only thing that priority is advertised as doing is making your driver exclusively deliver your food.
If you don't choose priority, you'll probably end up waiting for the driver to pick up/deliver other people's food along the way.
It doesn't make the restaurant prepare the food faster. It also doesn't allocate you a driver more quickly.
It just means that the driver goes straight to pick your food up, then straight to you to deliver it.