Geometry in nature arranges the shapes of the molecules and crystals that make up our bodies and the physical cosmos. It is the key to the creation of the universe. A good primer on this subject is Michael Schneiders interesting book A Beginner's Guide to Constructing the Universe. In his introduction, he says: "It's a shame that children are exposed to numbers merely as quantities instead of qualities and characters with distinct personalities relating to each other in various patterns. If only they could see numbers and shapes as the ancients did, as symbols of principles available to teach us about the natural structure and process of the universe and to give us perspective on human nature."
Studying and meditating on geometry helps us to better understand the laws, patterns and blueprints within nature. As we are part of nature, it can help us key in to and become more of our true selves, the magnificent spiritual beings who we really are. But if you are not into that, just studying the wonders and beauty of geometry is a healthy and thoroughly enjoyable past time anyway!