Often the nervous system is considered as a seperate 'brain' and the rest of the nervous system. However this is not entirely true. Although the cerebral cortex stores most of our 'memories' which we can bring to mind, the whole nervous system stores the memory of repeated body movements. (i.e. your if you've been doing aikido long enough, it is your body which remebers the techniques, not your brain).
Also, the centre is also the centre of gravity. As such, realising this as our centre enables us to keep balance more easily (because we can then move our body around this centre, rather than around another point).