Motions in a fluid that result in the transport and mixing of the fluid's properties. In meteorology, convection usually refers to atmospheric motions that are predominantly vertical, such as rising air currents due to surface heating. The rising of heated surface air and the sinking of cooler air aloft is often called free convection. (Compare with forced convection.)
WRCC Climate and Weather Terms Glossary

The rising of warm air and the sinking of cool air. Heat mixes and moves air. When a layer of air receives enough heat from the Earth's surface, it expands and moves upward. Colder, heavier air flows under it which is then warmed, expands, and rises. The warm rising air cools as it reaches higher, cooler regions of the atmosphere and begins to sink. Convection causes local breezes, winds, and thunderstorms. 
NASA Earth Observatory

Convection - Process by which, in a fluid being heated, the warmer part of the mass will rise and the cooler portions sink. This is also a a component of the theory for continental drift, in that the circulating movements of crustal materials push the continents apart.
[Journal of the Atmospheric Sciences. v 46, 1540, 1989.]
[Journal of the Atmospheric Sciences. v 45, 2641, 1988.]
Atmospheric Chemistry Glossary