Feedback from both Yamaha and Ducati riders indicate that the benefits are not clear, but various reports state that the intention is to add front downforce to reduce the tendency of the bikes to wheelie.
Unlike in the automotive world, wings cannot easily be used to add downforce to increase grip and cornering speed. As the motorcycle (and wing) leans, the forces from the wing act to add cornering load as well as vertical load, and the extra grip offered by the wing only goes to offset the increased cornering load. That said, there are some interesting patents and studies that detail ways that wings (both fixed and movable) can be used to generate more vertical than lateral forces as the bike leans, so the extra grip does not come at the expense of additional cornering load.
Data that I have from Jodi Christie's superbike at high-speed tracks such as Canadian Tire Motorsport Park gives some more insight into aerodynamics and how wings could be beneficial in other ways. Motorcycles typically have aerodynamic lift at speed, generated by the air passing over top - just like a gust of wind can pick a piece of plywood up off the ground. As well, motorcycles have more lift on the front end than the rear end, because the aerodynamic drag acts on a virtual point high above the ground. Imagine trying to ride your bike with a sail sticking way out the top, and how easily it would wheelie as you went faster.
Looking at suspension load and travel at various speeds on Jodi's superbike, it's apparent that lift has a significant effect on suspension travel at high speeds - as much as a 15 mm decrease in front suspension travel at the end of CTMP's long back straight can be attributed to front-end lift. This in turn affects geometry and how the bike behaves in slow turns compared to fast turns.
One parameter we look at from data is dynamic trail, and how it changes as the bike goes around the track. As the front suspension compresses, under braking for example, rake decreases and this reduces trail. On corner exit, the front suspension extends and the rear compresses, increasing rake and trail. Dynamic trail is a large part of what gives the rider the "feel" of the motorcycle, and we typically look for certain, consistent values given certain other parameters. But, due to lift at higher speeds raising the front of the bike and adding rake and trail, this consistency cannot be obtained at some tracks. The bike has a different feel and response in the different corners, and a compromise must be made in the setup.
If wings were used to add downforce at speed, front-end lift would be reduced, and dynamic trail could be made more consistent from corner to corner; this compromise in setup perhaps wouldn't have to be made. I am sure there is more to it than that at the MotoGP level, but I can see how even this one benefit would make using wings worthwhile.