What was the concept behind using the composite structure?
Evolving technology. It would have been fine except that there wasn't a long established history with composites at that time, so big factors of safety were heaped onto the design requirements which made everything way too thick and heavy. No surprise that when the two that were built went to Edwards for testing that the planes had lousy acceleration compared to the basic F-16. However, they did have a smaller turn radius due to the higher lift of that big wing.
F-16XL (aka F-16E at the time, they subsequently used the "E" for another variant) was originally called "SCAMP" = "Supersonic Cruise ... Hell I forget
. It was intended as a medium/high altitude interceptor. When the AF showed no interest in that, it was repackaged as a strike/interdiction dump truck just like the F-15E. Pretty silly when you consider that the low wing-loading made for one really bumpy ride down low. The AF was unimpressed and went with the Strike Eagle, a much better platform. If I recall correctly, the XL did have better range though because of all the fuel in that wing.
Funny story:
When the first XL was wheeled out for a photo shoot, they decided to unhook the tractor and tow bar to keep them out of the shot. Well everything about the program was behind schedule, including the radar, so the nose was empty. As soon as they unhooked the tow bar, the plane promptly sat back on it's tail.
Well obviously that was no way to take a picture, so eventually they had enough shop guys hanging on the front of the airplane to pull the nose back down. They hooked the tow bar back up and took the pics with it attached.