Why does boiled water steam more when it is taken off the heat?

When water boils, it is because all of the molecules are being provided with the energy necessary to change phase, from liquid to gas (water vapor).

The addition of energy (heating) allows the molecules to break their bonds and form water vapor, commonly known as steam (a process known as evaporation). The atoms in the water vapor carry away this heat energy as they rise higher into the air, before quickly losing this energy to the surrounding air.

The molecules still inside the bulk of the water should theoretically all do this, if other factors didn't interfere. The energy is transferred from most of the molecules into the others; these are the ones that evaporate. So as these molecules evaporate, they take heat from the rest of the water with them. The convection currents in the air absorb this heat and prevent its return, and your water cools down.