How do the ingredients in baking powder work?
Baking powder is like a fast-acting yeast; it is used to infuse air into baking mixtures by way of carbon dioxide bubbles, created by a base reacting to an acid. Baking power is made of three different parts:


An acid 
A base 
A filler


All three need to be dry powders that can be mixed together, common ingredients are cream of tartar (acid), baking soda (base) and corn starch (filler). The role of the acid and the base are to combine together to produce carbon dioxide bubbles when reacting with water or other liquids. The filler helps keep the baking powder dry, so that it remains free-flowing and so that the base and acid don't get moist and interact in the container. 

Resources:


This article explains the reaction process in further detail: http://recipes.howstuffworks.com/tools-and-techniques/baking-powder.htm
This piece  provides further insight on different types of baking powder, it's history, substitutes, etc.: http://m.cooksinfo.com/edible.nsf/MobilePages/baking-powder