House termites have wings during certain times of the year. These termites are called alates. These termites are members of the reproductive caste, and are fully developed males and females.
Each termite colony is founded by a pair of these alates, called the king and the queen. In turn, the colony produces another crop of alates in the fall or spring. Their job is to leave the parent colony, mate and form new colonies. After they've flown away from their old nest, they break off their wings and seek mates.
Winged termites are often confused with winged ants, but termites have robust bodies without waists and have wings that are the same size.