Symmetry comes from Greek - agreement in dimensions, due proportion and the arrangement in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definition. That an object is invariant to any of various transformations; including reflection, rotation, or scaling. It is easy to see because one half is the reflection of the other half.
The most familiar type of symmetry for many people is in science, art, architecture, music, and nature. The best example in nature are the butterflies. You'll find every spot on both of their wings. Also in Jewelry, people love the Symmetry. One of my teachers said that when you add gemstones, you must have the same amount on each side. Sometimes I do it but sometimes I like the difference. I don't always like Symmetry, that's the reason in my jewelry you will find an asymmetric piece, say, with a gemstone only on one side, amorphic design, that's the beauty of "one of a kind" piece. Are you a Symmetry person or an asymmetric?