A typical early game scenario might be that you have a large supply of dirt and water, and need to cook Mush Fry for food.
This involves two different cooking stations: the Microbe Musher to make Mush Bar, and the Grill to fry Mush Bar into Mush Fry.
Let's say you have 1 person assigned to cooking and forbid people from eating Mush bars, allowing them only to eat the end product, Mush Fry. This increases the number of calories they get, improves morale compared to eating Mush Bars, and is safer since frying removes bacteria.
If your priorities on the Microbe Musher and Grill are set wrong, so that the Musher has higher priority, then the cook will make Mush bars forever, never start frying them, and everyone will starve since you have a large stockpile of forbidden Mush Bars.
If the priorities are set so the grill has higher priority, the cook will make 1 Mush bar, then fry it, then get back to make 1 new mush bar, fry that one, and so on, alternating between the two stations and always frying a mush bar if one is available.
Another example would be where you want to prioritise between two recipes in the same station. Since this is not possible, you could build for example two Microbe Mushers, set one to high priority to make Liceloaf, and the other to lower priority to make Mush bars. As long as Meal Lice is available, Liceloaf will be made, but when you run out of it, you have a fallback of mush bar production which is worse food but still keeps people alive.