Dutch process cocoa is an odd duck, so to say. The main reason to use it is that it is chemically non-reactive, meaning that, in baking, it's neither acidic nor basic. Considering that baking is nothing more the a pleasantly edible version of chemistry, having a non-reactive version of cocoa flavor is invaluble.
The chemical non-reactivity is achevied through treating the original cocoa with alkali to neutrelize the natural acids. In general, when you see dutch process cocoa, the recipe will use baking powder rather than baking soda as a leavener, since the latter requires an acidic partner to make things rise.
Dutch proces cocoa has a more "delicate" flavor than its more bitter and acidic non-dutch compatriot. It finds itself in a lot of European recipes.
If you're an avid and experimental cook, you can adapt many recipes to a chocolate version with the help of either dutch process cocoa powder or regular cocoa powder. Just remember, when a baking recipe uses baking powder, you should use the dutch process version. If the recipe calls for baking soda, go with the regular. How much you should add depends on how much of a chocolate punch you want. In my average brownie recipe, I use 12 tablespoons to achieve the flavor I want, but I'm a big chocolate fan.
Dutch process cocoa can also be used instead of melted unsweetened chocolate. 3 tablespoons cocoa and 1 tablespoon of oil roughly equates to one square or one ounce melted unsweetened chocolate. If a recipe calls for bittersweet melted chocolate, add to this mix one tablespoon and one-half teaspoon plain white sugar.