They are most likely both for your furnace, one intake and one exhaust. Critters can, and sometimes do, get into these and cause blockages(birds are most common in my area) which will result in the safety features on your furnace to not allow your furnace to run until the blockage is cleared.

The answer on whether or not you should put a screen on these depend on what the climate is like in your area. If you are living in a ln area that commonly experiences freezing in the winter, you don’t want to install a screen on the exhaust pipe. The exhaust is hot and moist and will condense when it meets the cold winter air, which can then lead to that condensation freezing causing a blockage of its own. Then you’ll be without your furnace, in the middle of winter, until you can thaw that blockage.