What are the advantages of a lid on a barbeque?
The lid can do one of three things:


Keeping the lid down increases the temperature of the air in the grill. This means that in addition to cooking with the direct heat of the coals, you are also cooking with convection of the air. This won't happen with the lid up. 
In a charcoal grill, the temperature the coals burn is based on the airflow through the grill. Open is as hot as it will go (assuming the bottom vent is also open). By closing the lid and altering the airflow, you can control the temperature of the grill. My grill can keep fine temperature control between 200F-700F depending on how you set the airflow. 
Which leads us to smoke. It seems obvious that if you are smoking, you will impart more flavor by trapping the smoke with your food rather than letting it float in to the sky. Additionally, you want wood to smolder not burn for your best smoke production. This works better at a lower temperature (see #2).