The covers serve a couple of functions. One is for better MPG in the way of better aerodynamics. With the cover off the engine bay becomes a high pressure area because the are going under the car gets trapped. This is why you see the hood lifting more when the cover is removed. Another reason is to provide better cooling. You want as much air as possible to go through the grill to hit the radiator and inter cooler. The under tray works to keep that same high pressure area forming under the hood, which reduces the amount of air that can flow through the radiator. A final item, which is probably more trivial so to keep water and rain from getting into the engine bay more so than you would have without the under tray.
Out of all of those items, better highway MPG is probably the biggest factor, though I'm sure that the cooling system was also designed around having the under tray. You are going to see many many more underbody aero items on future models because of the higher EPA ratings in coming years. My 2013 F150 actually has a little chin spoiler under the bumper, which is meant to deflect some of the air from getting into the engine bay, again for better highway aerodynamics. I wouldn't be surprised if we start seeing full body under trays on regular cars and not just super cars in the near future as manufacturers are going to have to pull out a lot of tricks out of their hats to hit future economy requirements. Engine advancement is only going to do so much. These aero mods will also be a lot cheaper to implement before you start seeing more all aluminum and composite cars working to get the weight down while having to meet ever tougher crash test requirements and inclusion of more electronic safety gizmos, which keep adding weight back into cars.
