The negative rod is brought close to the uncharged grounded sphere. Since unlike charge are repeled, the electrons are "chased" out of the sphere and leave through the grounding wire. When the ground and grey charged rod are removed (must be removed in this order, why?) the green sphere is now poitvely charged.
A negative rod can charge an object positively by induction (opposite to harging by contact).
A positive rod will cause an object to become negativel charged by induction (just the opposite occurs to above).