Air filter covers are kits out there to modify your air filter allowing more air in, but still filtering it so no damage is done. The cover also keeps dirt out of the engine by filtering it through the air filter. Without the air being filtered, you’ll get dust and dirt of various kinds down inside the engine which will damage the engine over time.
Without the cover, you can get more air into the engine more quickly allowing it to run faster, but at the same time damaging the engine more.