Herman Merte, a professor emeritus of mechanical engineering at the University of Michigan at Ann Arbor, explains:
What one sees drifting above a hot bath—often called “steam”—is in fact tiny drops of liquid water that have coalesced out of the gaseous mixture of air and water vapor above the fluid’s surface. The vapor, itself an invisible gas, arises from evaporation, whereby water molecules escape from a liquid. Evaporation is a slower process than boiling but is accelerated when water heats up (gaining increased energy).
The conditions under which invisible water vapor condenses into visible mist depend on the ambient temperature and the amount of water vapor in the air. Compared with cold air, warm air can hold more water vapor before becoming so saturated that condensation occurs. This property explains why a bath—or a cup of tea—emits more visible steam on a cold winter morning than on a hot summer afternoon.
Note: This article was originally printed with the title, "How does bathwater well below the boiling point give off steam?"