That thing on the passengers side is there to relieve the air pressure from inside the car when you close the doors with the windows up. Obviously when everything is closed and you leave your car a positive pressure builds inside the car when you close the door, that could make it harder to close the door all the way. That vent is there to release the air as you close the door, there's little rubber flaps over the vent to prevent water from getting inside when it rains.
When you can have all the doors and windows closed, trunk too. then go to the passenger door, and just open it and close it while keeping an eye on those vents, you'll see the flaps move up and as air rushes out from the car.
It looks like you have some damage on the drivers side there and chances are the vent on that side was broken or something, It looks like someone just patched it up but not sure how they did it. I've had my rear bumper off numerous times and I know for a fact I have those vent deals on both sides.