Baking powder is normally made of three different parts:
All three need to be dry powders that can be mixed together. For example, soda bicarbonate (a base), cream of tartar (an acid) and cornflour (the filler) are three common ingredients. In school, you may have done the experiment where you mix soda bicarbonate (a base) and vinegar (an acid) and get a bubbling reaction. Baking powder works the same way. When you add water to baking powder, the dry acid and base go into solution and start reacting to produce carbon dioxide bubbles. Single-acting baking powder produces all of its bubbles when it gets wet. Double-acting baking powder produces bubbles again when it gets hot.
If you want to prove to yourself that this is how baking powder works, simply try mixing a teaspoon of baking powder into a cup of hot water. As long as the baking powder is fresh, you will definitely see the reaction! Many recipes call simply for soda bicarbonate rather than baking powder. Usually these recipes use some kind of liquid acid like buttermilk or yogurt to react with the soda bicarbonate to produce the bubbles.
The reason why people often prefer baking powder to yeast is because yeast takes so long -- usually two to three hours -- to produce its bubbles. Baking powder is instant, so you can mix up a batch of biscuits and eat them cooked about fifteen minutes later.
Now that you understand how baking powder works, you can understand two things you often see in recipes:
Many recipes instruct you to mix all of the dry ingredients together and then add the liquid. That keeps the baking powder from reacting until the end of the mixing process.
Many recipes tell you to mix only briefly -- just until the ingredients are moistened. That minimizes the escape of the gas from the batter. If you were to stir for a long time, the reaction would end and the stirring would have allowed the bubbles to escape.