Okay, I think I've cracked it. It seems to be for two reasons ... firstly, to allow the bird to rest its neck muscles ... and secondly, pretty obvious really, to shield the bird's eyes from bright light (sort of like pulling the pillow over your head!).
Actually, birds don't tuck their heads under their wing. Instead they rest their heads on their backs while they nuzzle their beaks into their back feathers. Sleeping with their head tucked on their back allows birds to rest their neck muscles and also makes for better heat conservation.
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