Here is a photo that perfectly illustrates the concept of backfilling. You can see that the frame once contained brood in the center with an arc of nectar above and to the sides. But now, most of the brood has emerged and the empty brood cells, which are slightly darker, are being filled with nectar instead of more brood.
When this happens in spring, it means the colony is getting ready to swarm. In fact, backfilling is the most useful indicator of swarming because it happens early enough that a knowledgeable beekeeper may be able to prevent the swarm.
Bees backfill the brood nest to shrink it. Without so many places to lay eggs, the queen slows her egg production and the brood nest contracts. This is important because after the swarm leaves, the brood nest will be small enough that the remaining bees will be able to care for it. Backfilling provides a way of scaling down the entire brood-rearing operation so a smaller workforce can still get the job done.
One of the most effective ways to counter backfilling is to open the brood nest. Opening the brood nest is accomplished by adding empty frames between frames of brood. So while the bees are busy contracting the nest, you go in and expand it. When a breach in the nest occurs, the bees go in and draw comb and the queen fills it with eggsall of which delays swarming and may prevent it altogether.
To avoid chilling the brood, opening the brood nest should only be done when there are enough bees to cover the expanded nest. However, backfilling normally occurs when a colony is preparing to swarm, which means there are usually plenty of bees and moderate nighttime temperatures.
Thanks, Nan, for sending a great illustration.