Cursors tell you what will happen if you send your civilian to that terrain tile. For most units, a hammer cursor appears over spaces where that unit could move and do work.
The Prospector has a special cursor, an eye that appears over places he can search for minerals. The Engineer also has a special cursor, the railroad track cursor which appears over spaces to which he could build rail. When the hammer cursor appears over the Engineer, it indicates that he could construct a depot, port or fort in his current space.
If you see a green arrow, the civilian can move there, but he will accomplish no work this turn.