The liquid inside a hand boiler does not actually boil. The "boiling" is caused by the relationship between the temperature and pressure of a gas. As the temperature of a gas in a closed container rises, the pressure also rises. There must be a temperature (and pressure) difference between the two large chambers for the liquid to move. When held upright (with the smaller bulb on top), the liquid will move from the bulb with the higher pressure to the bulb with lower pressure. As the gas continues to expand, the gas will then bubble through the liquid, making it appear to boil. The fact that the liquid is volatile (easily vaporized) makes the hand boiler more effective. Adding heat to the liquid produces more gas, also increasing pressure in the closed container.
