The mesh on the left is before morphing; the mesh on the right is after morphing.  The icon for 2-plane symmetry is two rectangles perpendicular to the symmetry system's selected axis and subsequent axis.  You can think of these rectangles as mirrors. The highlighted handle is moved.  Note how only the handle at the lower left has been selected and how the other three symmetric handles are automatically moved symmetrically.  This type of symmetry is very useful for objects symmetric across two perpendicular planes.