An 'absconding swarm' refers to a swarm of bees that are completely abandoning their hive.
Normal swarms are simply a part of the reproductive cycle of bee societies. A queen bee will lead a swarm from the old hive, taking with her the older generation of worker bees and drones. They will leave the younger bees behind to continue the colony in the original hive; this will usually include a queen or at least a developing queen, the entire brood (the larvae and pupae), and enough bees to take care of everything until the brood starts hatching and replenishes the hive.
In an absconding swarm, all the bees that can get up and go, do so. This is a drastic measure, and is not a form of reproduction, as the entire brood is left to die. This may be done as the result of attacks on the hive (from humans, dragonflies, ants, snakes, mice, etc.), starvation, or disease (such as foulbrood). Absconding swarms are very rare; a colony will usually die out before vacating the hive.
Africanized honeybees are more likely to form an absconding swarm when resources are scarce than are European honeybees, sometimes descending on farms and other human habitations where there are steady water supplies or food sources.