There are basically two different ways to get cocoa powder out of the beans. One, called "the Broma process," produces so-called "natural" cocoa. This is reddish-brown and very bitterly flavored. In my experience, most of the cocoa powder on the market is "natural."
The other process is called "the Dutch process," because it was invented by a Dutch chocolatier in the 19th century. It involves using an alkali to extract the chocolate. An alkali (also called a base) is the opposite of an acid -- it has a high pH instead of a low one. A very strong alkali with which you may be familiar is lye. A weaker alkali, that you use all of the time, is baking soda.
Cocoa produced with the Dutch process is called "Dutch-processed cocoa," or "cocoa processed with alkali." It is a darker brown in color, less reddish. Its taste is smoother and less bitter.
A lot of the cocoa powder on the market is a mixture of the two kinds. It is hard to find Dutch-processed cocoa, in my personal experience.
Both kinds of cocoa are perfectly safe, and don't contain any weird chemicals. Despite the name, "natural" cocoa is not less processed than Dutch-processed; they are both very processed foods (so is sugar -- processed isn't necessarily a bad thing).
The two types of cocoa have slightly different uses. I generally use only natural cocoa when baking. I prefer Dutch-process to make hot chocolate.
[I kind of fibbed to you at the beginning, to keep things simple. The Broma process is the most commonly used way of producing natural cocoa, but any extraction process that does not use alkali makes natural cocoa. Natural cocoa predates the invention of the Broma process.]
Edit: According to Wikipedia, Dutch-processed chocolate has fewer antioxidants, so less of a health benefit. That makes sense to me. So, that's another difference