Bees increase the number of their colonies by swarming. In early spring, numbers of young bees are reared until the hive becomes crowded. Then drones are reared, and queen cells are built. The old queen and a part of the bees leave the hive to seek a new habitation. The hive, however, is left full of brood which is hourly hatching, and soon becomes as populous as ever. A young queen hatches in about eight days after the old one leaves, and if she is permitted, will destroy all the other embryo queens. If the bees, will to swarm again, they prevent her from doing this, and then second, and third, and often more swarms come out, led by these young queens.
A swarm of honey bees will settle on a tree branch or bush etc. whilst a few scout bees locate a new home. It is at that stage that a beekeeper can oftentimes collect the swarming bees by putting a suitable container such as an empty beehive below the settled swarm and encourage them to use that as their new home if the queen will accept it (if you are not an experienced beekeeper it is very much recommended that you do not attempt to capture a settled swarm of bees yourself).
(photo licensed under GNU Free Documentation V1.2)