This stylish desk ornament is a practical example of how gas expands when heated. When you clasp your hands around the base of the desk toy the coloured liquid appears to boil.
This is the result of Charles' law which was created by Jacques Charles in 1787. Charles discovered that the volume of a gas is proportional to its temperature. Therefore when gas is at a constant pressure, such as inside a Hand Boiler gadget, the gas' volume increases as the temperature increases.
So in plain English, the heat from your hand causes the gas inside the gizmo to expand pushing the liquid up the spout.