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The 9 Angles or Circles of Attack is one of the most important concepts in the martial arts.  Just about every technique, whether it be a throw, joint lock, kick or punch, follows along one of these angles, or variations of these angles.  If you understand this concept, learning, applying, and thinking of attacks and defenses for situations that you have not practiced against will be easy.  It also helps to simplify your thinking; for example if you did not know about this concept defending against a ridgehand strike and a roundhouse punch might seem like to different attacks, when in fact the are almost exactly the same because they both follow on the same circle of attack.  This is useful because the less you have to think about in a fight the faster you will be and the faster you will react.  The picture below shows the nine angles or circles of attack.   It is not a very good picture and as soon as I find a better one it will be here.  The 9th angle comes from the center straight out and away from the body, although you can't really see it on this picture.