I understand that food cooks differently in a double-boiler than when cooked "directly" - but don't know why that is.
How does utilizing a double-boiler change how food cooks?
Use of a double boiler limits the maximum temperature the food being cooked can reach. The water in the lower part of the double boiler can only reach 100*C (212*F) before it boils. The food being cooked, therefore, can only reach a maximum temperature of 100*C (212*F). It can't go over that until all the water in the lower pot has boiled off.
The double boiler maintains a steady, even temperature due to being heated by the surrounding liquid. Basicallly, (assuming the two pots don't touch) the heat in the internal pot will never exceed the boiling point of the water surronding it. Further, the liquid surrounding the internal pot has an insulating effect that makes temperature changes more gradual. When exposed to direct flame or heating element, the pot can do so easily, and temperatures may fluctuate more quickly.
The steady heat provides a good environment for tempermental foods/sauces that require a very specific temperature. Chocolate and Hollandaise are good examples of this.