Most systems of martial arts teach techniques. This is ok, but the problem is that when the situation is not clear cut (they grab you a bit differently, strike more wildly, etc., etc.) then it can be hard to adapt the technique -- especially on the fly. Many systems address this by having a lot of techniques, often numbering in the thousands, to cover every possible scenario. Moreover, this approach makes it really hard to relate various similar techniques. The hallmark of a lot of Masters in such systems is that they can tell you which techniques can be grouped together.
A better way in the long run, but one that has less immediate return is to teach via principle. In this case, one has a specific optimized movement and the training is for facility, so that applying the movement in every conceivable situation is the goal. This is summed up by saying that on trains for facility, not ability. In other words, having some very specific ability (like being able to apply one specific throw off a grab), while nice, does not mean you can generalize. You want as much chaos as possible in training. Random grabs, weird angles, extra attackers, bad terrain you name it.
We have principles as the basis for techniques plus a training paradigm (8 directions) to make sure we get a good mix plus flow drills to get the really high repetitions without numbing your brain too much.
There is also a generic listing of categories of techniques and students want to know what the difference is. The categories are simple classification whereas the principles have some profundity about body usage. By analogy, a knife would be a type, but we have a Swiss Army knife. So, for example, a te kagami can be used as a throw, pin, lock etc. Generally, there all HDR principles fit into multiple categories, which is why they were chosen. This makes the system much more compact, since every principle does at least double duty. This was part of the genius of setting up the system this way.
This brings me to why the belt ranking requirements are laid out the way they are. A lot of HDR schools simply teach the entire kata at the basic level and just require that the student do it progressively better at each level, adding more henka. I think it ends up being more accessible for the student to focus at each belt level on specific principles. This means that, say at green belt when you are to use otoshi you should attempt to apply it everywhere and are a good compulsive-obsessive about it. For instance, dropping your weight into strikes, being aware of how your bodyweight controls someone for a floor pin, setting people in motion for other techniques (such as off-balancing) and, of course, standard body throws. The requirement for the kata then means not that you can just do it, but that you understand it very well and why each part of the kata is there. A not uncommon part of the belt test is to have you teach the kata you are required to know to a lower belt.
Here is the list of principles for shodan and some commentary about each. You should refer to the standard kata manual for the art for all the details.
Hakko dori. Escaping through the opening. Generally this means that for any grip or grapple you figure out how to expand it, render it mechanically less efficient then exit through the hole you made. It is also a strategic principle, so that for example, if you are blocked by several people, you create a gap between them.
Hakko zeme. The push, or unbendable arm. A supremely useful concept and one that you can get a great deal of mileage from. The kata is a bit of a head scratcher at first. While rather hard to do, this trains this at many, many angles and makes it so that you can get this whenever you need it. It also forces you to keep good body structure to the floor. A large part of this is showing one option if uke stiff-arms you. If he does not, then you are permitted to hit as hard as you like. Repeat as necessary.
Atemi. Striking. The basics of all striking are here: off-lining, off-balancing and pulling your opponent into the attack. Note that the seated version of the strike is to the face (kao ate) while the standing version is to the neck (tachi ate).
Aiki nage/hiki nage. Two-point projection throw. This is about stumbling, not throwing. Projecting through two points will cause your oppone to stumble – that is really the hard part of any throw. Once you have him stumbling, throwing can be effected by sticking out a foot, for example (all sweeps are applications of this principle) or any of a variety of other methods. For uke's part, this is the first throw from a standing position and when receiving, you should be sure to roll. This teaches you what to do if you are stumbling and are having your head pushed into the floor – roll.
Te kagami. (literally "hand mirror") Wrist twist to the outside of the body. The key to pull out of this is to attack the thenar (the pad at the base of the thumb). This allows you to control the radius (the forearm bone under the thumb) which inturn allows you to control the arm and ultimately the shoulder.
Otoshi. Dropping your weight to set uke in motion. Again, one of the basic techniques, in the sense that it will occur in virtually every movement you do. The beginner's version of this is a very gentle throw, whereby uke ends up on your back and you simply look at the ceiling to remove support. A more severe version actually does the drop and can make uke do a truly impressive aerial. The movement of dropping one's weight pervades the art.
Shodan osae dori. Using the arm like a stick. It can be used as a pin (the osae dori kata) or for throwing (kubi shime dori, uchi komi dori). Do not put a premium on attacking the joint, but using the arm against uke.
Yoko katate osae dori. The complement to te kagami teaches you one way to control the pinkie side of the hand. The first movements of the kata are there to position uke. They are also quite practical since they show one way to lock up the opponent while you seek position.