The mesh on the left is before morphing; the mesh on the right is after morphing.  The icon for 3-plane symmetry is three rectangles perpendicular to all three of the symmetry system axes.  You can think of these rectangles as mirrors. The highlighted handle is moved.  Note how only the handle at the lower right has been selected and how the other seven symmetric handles are automatically moved symmetrically. This type of symmetry is very useful for objects symmetric across three perpendicular planes.