Reproductive swarm is one way that termites start new colonies. Budding or splitting a colony into smaller pieces is another way. In a mature termite colony, sexually mature winged reproductives (or alates) are produced. When the time is right (see below), these future queens and kings leave the colony, flying low for only a short distance. The purpose of the swarming event is (1) to disperse termites to new areas, although most don't travel far, (2) to find a mate, hopefully from a nearby related colony that is swarming at the same time, and (3) to then mate and establish a new nest. If a pair survives predation and successfully mates, they search for an appropriate nest site in soil or wood where the new queen begins a lifetime of laying eggs and producing more termites.
The number of swarmers produced by any one colony varies with the species and the age and condition of the colony. A subterranean termite colony doesn't produce its first significant swarmers until the colony is 3 to 5 years old. Thereafter, a mature colony will usually produce winged swarmers every year and tends to produce more swarmers as the colony grows. The same mature colony can produce as many as four swarms over a one month period, with the first being the largest. So, the size of any one swarm is not necessarily an indication of the size of the colony. In each location, thousands of swarmers can emerge from a number of different colonies at the same time. It can be quite a sight but may only last for minutes. The actual swarming event is tied to weather conditions of temperature and humidity (except not so much inside heated buildings). It is usually a rain event that triggers subterranean termites to swarm. The same termite species may swarm at different times of the year in different parts of the U.S. Nighttime swarming species are attracted to lights.
If conditions aren't right for swarming, alates can wait in the colony or in mud swarming tubes for days until rain and temperature cooperate. In the colder, far northern U.S. and Canada, termites rarely swarm at all, except sometimes in heated basements.