This toy consists of two glass bulbs connected by a glass tube. The yellow liquid is some kind of volatile liquid. So the two glass bulbs contain two bodies of trapped vapour separated by its own liquid form.
When the palms warm up the lower bulb, the increased temperature causes the yellow liquid to evaporate into the lower bulb. The increased number of vapour molecules in the lower bulb increases the pressure in the lower bulb, thus pushing the yellow liquid up the tube. When all the yellow liquid have been pushed out of the way, the vapour simply bubble their way up the glass tube.
So the yellow liquid was not boiling. The vapour forcing their way from the lower bulb to the upper bulb made it look like boiling.
Wrapping the palms around the upper bulb caused evaporation to happen at the upper bulb instead, thus reversing the direction of bubbles.
When dipped in hot water, evaporation in the lower bulb drove up the pressure in the lower bulb. On the other hand, when dipped in cold water, condensation in the lower bulb drove down the pressure in the lower bulb, causing the higher pressure in the upper bulb to force the liquid and subsequently vapour bubbles down the tube.
Further reading: http://en.wikipedia.org/wiki/Hand_boiler