Keeping your center...
Wow! This is one of those concepts that has a lot of layers of meaning.
The most basic definition is that your center is the center of gravity for your body. It's best to think of it as a point about two to four inches up from your belly button. Being aware of your center is important in all sorts of physical activities, from rifle shooting and soccer to balancing on a ladder or lifting heavy things.
In Aikido, in the techniques that I know, it's best not to let your center get too far away from being over your hips. For example, last Wednesday, I was working on shomenuchi kokyonage which involves a tenkan turn. During the tenkan, I was leaning over into my uke and the technique didn't feel very good. After I realized my error, and focused on maintaining my center, the technique felt a lot better.
In essance, my center became the center for the two of us.
A deeper meaning refers to the concept of a relaxed awareness and a sense of being grounded. In Tao, there is an idea of being relaxed, but ready to deal with what life throws at you. You don't just react from situation to situation without having as sense of your own position or self. Neither do you focus so much on your self that you don't notice what's going on around you. Nor should you focus on what's going on around you with a frame of mind that tries to fit those things into a preconceived notion. Nor should you deny what's happening because you don't like it.
Being centered in the Tao sense is about accepting things the way they are; going with the flow without loosing yourself in it. These same concepts translate well to Aikido.
Most of my understanding of this topic comes not from Aikido, but from my studies in exercise and sport science at Penn State (now called kinesiology -- the study of movement) and my study of Eastern thought like Tao and Zen. I'm axious to read how others with more Aikido experience respond!
[Edited by jxa127 on July 24, 2000 at 12:22pm]