Just what the title states--given an absurdly large number of assignments to perform in a limited time-frame we usually attempt to do the most important ones first. Is this ability to define and execute by priority a universal feature in all sentients, or is it a socially learnt behaviour of us Homo sapiens?
There is a very simple experiment you can do that will demonstrate that animals prioritize. Give a dog two bones. Preferably one which is more tasty than the other. Say one has more meat on it. The dog cannot eat both at once and you will observe it choosing one over the other. This is a clear example of prioritization.
Again with a dog, try observing one greeting two people it is fond of. If you and a friend stand a few meters apart when the dog comes up to you, the animal will choose to greet one of the humans first. Prioritization.
Any animal, or plant, fungus, bacterium or archaeon for that matter, that is ever presented with a choice between two actions during its lifetime, will have to be able to prioritize in order to chose between them. Clearly they can as our world is not strewn with, for example, panicked, confused looking squirrels trying desperately to chose which tree to climb.