The mesh on the left is before morphing; the mesh on the right is after morphing.  The model is a hollow sphere made with solid elements.  The icon for spherical symmetry is a sphere centered at the symmetry system origin. The highlighted handle is moved.  Note how the handles act on the mesh as if they were spheres centered at the origin.  This type of symmetry is useful for changing the shape of spherical objects while keeping their spherical shape intact.