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Symmetry comes from a Greek word meaning 'to measure together' and is widely used in the study of geometry. Mathematically, symmetry means that one shape becomes exactly like another when you move it in some way: turn, flip or slide.
Symmetry also has an aesthetic meaning, although this is harder to define; artistic symmetry is beauty found in a pleasing and regular form. There are many kinds of symmetries, from the left-right symmetry of a face (left), to the five-fold symmetry of a starfish (center), to the complete symmetry of a circle (right). These sorts of symmetries are also seen in physics theories, leading some physicists to describe the equations as beautiful.