Many birds regurgitate food for their young, but eagle parents actually tear off small bits of food and gently place them in the eaglet's mouth. The only regurgitation adults do is to expel small pellets of undigestable food (like fins and feathers).
When someone mentions pellets, most folks think of owl pellets, but eagle pellets aren't as "interesting" as owl pellets. Owl pellets sometimes have the entire skeleton of the animal they ate inside. Eagles have strong stomach acids, so small bones are not usually found in eagle pellets. Also, eagles tend to pluck their prey more than owls do when eating.
As for the eagle chicks, after a few weeks they'll be able to tear off the food for themselves, and Mom won't have to do all the work.