Convection currents occur due to the density difference between hot and cold fluids. A fluid that is heated from below expands and rises. When this fluid becomes cool, it contracts and sinks. This continuous cycle of expansion and contraction causes convection cells.
Convection is the only one of the three heat transfer methods to involve the movement of matter. The other two methods, conduction and radiation, transfer heat between relatively stationary medium particles or without the need for a medium at all, respectively.
The decrease in density that accompanies heating is explained by the ideal gas law. At constant pressure, the temperature of a gas is directly proportional to its volume. As the temperature increases, the kinetic energy of the gas molecules or atoms also increases. The more energetic these gas molecules are, the faster they move. Assuming a constant average time for collisions between gas molecules, an increase in speed corresponds to a larger average distance travelled between collisions, which correspond to a larger volume being occupied by the same number of molecules.
Because volume is inversely proportional to density for the same mass, this increase in volume with an increase in temperature corresponds to a decrease in density. Less dense fluids float on top of more dense fluids, so the hotter, lighter gas floats on the cooler, denser gas. Similar principles can be applied to liquids, which undergo less expansion and contraction with heating and cooling respectively.