Apparently to birds of prey, they head is the most delicious and nutritious part.
After catching the prey the bird will rip the head off and eat it.
That is what the Osprey are doing.
With so many hungry mouths to feed he is taking the best part of the fish for himself to make sure he is well fed and healthy to keep up with the demand of fishing constantly. Then will bring the remaining part to the nest for the young.
Hope this helps.
Sorry about my earlier post, I wasn't sure if you meant the Osprey was returning with half eaten fish or leaving the nest with half eaten fish.