The concept of Ah! My Goddess is rather simple if you just hear a simple description of everything, but it doesn't take long to discover otherwise. One of the things that really got me into this series, was the complexity of the AMG universe. Fujishima has assembled an intricate system for the way the universe works. I don't think I've ever encountered any other story which cast the universe as a giant computer system, integrated with elements of magic. While this certainly adds to the enjoyment of Ah! My Goddess, it unfortunately seems really damn complicated for those who are not well versed in the series. The best way to gain understanding is of course to read all the manga. Of course that isn't always possible, so little sections like this can be fairly helpful to gaining insight into the AMG universe. This section won't go extremely in depth, but will mainly hit on key points and concepts.

l i c e n c i n g   s y s t e m

The Licensing system seems rather complicated, but once you get the hang of what thing refers to what, it all sort of makes sense (and makes a drivers license a piece of cake to understand). The licensing system refers to more than just goddesses. In fact, it seems like just about everything is organized in a much similar hierarchy. Goddesses, demons, and earth-spirits all follow this organization, so assumably everyone else does too.

Classes

License classes refers to the degree of precision in use of power. Think of it as a measure of skill in which you can use your power. Belldandy is a goddess first class since she has a lot of power, and precision. Skuld is a second class goddess because she has little power at all (so accuracy is not so much relevant), but keep in mind that her powers are still developing. Urd is a second class goddess because her accuracy is very poor, even though she is in fact more powerful than Belldandy. But of course who needs to be accurate when your just throwing big ass lightning bolts anyway? ^_^
Keep in mind that this only applies to skill in applying raw power, the classifications do not reflect skills in other areas, such as Skuld's abilities in making inventions, and Urd's know-how in chemistry. These skills are to some extent just as useful (if not more) than their respective goddess powers.

Type

The types come in two forms: Type 1 - regular, Type 2 - commercial. Little is really said about what it really means to have a commercial license, but presumably it has to do with what your job is. Belldandy has a commercial license. Assumably this gives her permission to travel between the Earth and Heaven. The manga somehow manages not to point out what Urd's license is, but it seems to be a non-commercial license (I'm guessing). But as system maintainer, she still has many permissions to access parts of Yggdrasil. Skuld does not have a license because she is so young. She is actually working to obtain a license. Skuld probably doesn't need a license since her job is system debugging, which is more akin to being a janitor more than anything.

Limitations

"Limited" or "Unlimited" refers to the level of power a one can use. This is somewhat deceiving since this refers to the amount of power a goddess is allowed, not how much power a goddess is capable of using. Even though Belldandy has an unlimited license, it doesn't really do her much good since the majority of her power is bound up in a seal (the earring in her left ear). The seal is sort of a safeguard against accidents since she has enough power to destroy the Earth herself. Urd has a limited license. Even though she has more power than Belldandy at her disposal, she isn't allowed to use it. With Urd's immense power, her ability to call forth more power by tapping into Yggdrasil, and having a short temper, perhaps it's better that she does have a limited license. Skuld's license is limited, even though she doesn't really have enough power (yet) to warrant limiting.

m a r k i n g s A very distinctive feature of Ah! My Goddess is the goddess markings on their foreheads. Exactly what are these markings you may wonder. The markings are supposed to manage the essential function of a goddess / demon / earth spirit. Whether the marking actually manages the function, or whether the marking simply reflects what the function of a goddess is, is much like the argument of whether the chicken or the egg came first. It does however suffice to say that the marking of a goddess, demon, or earth spirit tells about their function. You may notice that Peorth and Belldandy have similar markings. This is because they preform similar functions (but for different offices). Also a good thing too keep in mind, is that the markings are not written in stone, that is, the markings can in fact change should its wearer change functions. For example, when Urd became possessed by the Lord of Terror, her goddess marking became that of a demon (like Mara's mark). When Belldandy broke her seal (her goddess marking changed from a diamond to two triangles with a dot in the center.

The doublet system

Obviously, Goddesses and Demons are at odds with each other by their very nature. You would almost expect that there would be some sort of war between the two sides of good and evil, yet this is not so. In fact, nearly total balance is kept between light and dark. This is done through the doublet system.

A specific goddess's life is linked to a demon counterpart. Should one perish, the other will do likewise. The system goes even deeper in that no goddess or demon actually knows who their life is linked to, as those specific memories are wiped when they are children. Which is sort of interesting in itself that there is a sort of authority that has the power to create and maintain such a system for goddesses and demons.