Two leaveners are used to balance the flavor. They are balanced against each other to achieve the proper rise. When using both baking soda and baking powder, you use less of each than you would of either alone.
Baking soda reacts with acids to produce CO2. It will start reacting as soon as it's wet. If a dish has enough acid, you will only use baking soda to leaven it. The reaction with the baking soda reduces the acidity of the product to create the proper flavor balance of the final product.
Double acting Baking powder has two acid base reactions to produce CO2. The first is usually a wet reaction as with baking soda. This lightens the dough and introduces air pockets that will produce the initial oven spring as the hot air expands.
Single acting baking powders (such as home made ones based around baking soda and cream of tartar) usually do all ther leaveneing as soon as it gets wet.
The second reaction is heat activated, usually around 130 degrees and drives the rise of the batter to the proper level.
If you're cooking with buttermilk, yogurt, and such acidic ingredients, you'll use some baking powder to leaven the dish. Those aren't unpleasantly acidic and so some baking powder is usually ther to give enough rise to the final product as some of the flavor of the dairy should come through.