Leaveners make your baked goods rise. Heard of unleavened bread? It's flat--no leavening. You have to use some sort of leavening if you want something fluffier and lighter than matzo.
Leaveners fall into a three categories: biological, chemical and mechanical.
Biological Leaveners: We're talking yeast here, people! Yeast are little one-celled organisms that do two things: they eat sugar, and they turn it into alcohol and carbon dioxide. Yeast is used in beer and bread production, and often beer is referred to as "liquid bread." (So, if you need justification to do the 12 oz. curl, I'm helping you out)!
Anyway, in bread making, the carbon dioxide bubbles are trapped in the gluten strands (see Ingredient Function--> "Flour"), and that's what makes the bread rise.
Chemical leaveners: Powdered (generally) chemicals that give off carbon dioxide when in the presence of liquid:
Baking soda is one of these leaveners, and baking soda is also the reason that Alka Seltzer bubbles. All that "Plop, plop; fizz, fizz" is put to great use leavening slightly acidic ingredients (think buttemilk, natural cocoa powder and molasses). Baking soda is a very powerful leavener, and a mere 1/4 teaspoon is all you need, per cup of flour.

Baking powder is baking soda to which an acid has been added. This leaves the pH of the powder at 7, orneutral. Baking powder is used to leaven neutral batters, or batters that don't contain acidic ingredients.
Double acting baking powder has two chemical reactions. It releases some carbon dioxide bubbles when it gets wet (during initial mixing), and it emits more carbon dioxide bubbles when it's exposed to heat (in the oven). Using double acting baking powder can result in a higher and more even rise. The ratio of baking powder per cup of flour is roughly 1 tsp of baking powder for every cup of flour.
Mechanical leaveners: eggs and steam, friends. Eggs and steam. Baked goods that are leavened mechanically rise because a)you've either beaten enough air into egg whites or whole eggs (think angel food cake or genoise) that the air in all those millions of foamy egg bubbles will expand in the oven and make your cake rise, or b) there's enough water in the batter that will turn to steam and force a rise (think cream puffs and puff pastry).
**Chemical leaveners are the main way that American-style baked goods are leavened. While Americans certainly make yeasted breads, the majority of American cakes, cookies and quick breads are leavened with baking soda and/or baking powder. Mechanical leavening is the main way that European-style baked goods rise. Most pastry chefs on "The Continent" consider using chemical leaveners cheating. They also speak of off, metallic or chemical flavors in the final product.
And that is the lesson on leavening.