Possibly, they would move the litter from the birthplace to get them away from a place which may smell of blood from the birth, and attract predators. They may also move the kittens because the site they are in no longer feels safe to the mother cat. Perhaps they may also move them closer to a food source.
I believe it is to move them to a place away from humans and to keep them safe. Probably where they would not be accidentally stepped on. One time a cat of mine had here kittens outdoors and kept them in a place until she thought it was time to bring them inside for them to interact with humans. The day she decided was a day I was cleaning my car out. She brought her kittens, there were 3-4-one at a time and placed them on my car seat. Then I brought them in to the house.
They move them to a safer location for not only do they need darkness and quiet for sleeping but once they start moving around and getting out of their bed area they need to be close to getting back to mama in case of danger.