First, confirm that the explorer is selected. On the map he flashes with a white outline, and his picture appears in the toolbar on the right side of the screen.  

In Episode 3 the explorer was used to prospect. When used in the New World, he can both reveal hidden terrain tiles and prospect for mineral resources. 

Move the mouse cursor over New World terrain tiles already revealed. Over some tiles you will see the green arrow (deploy) cursor, and over other tiles you will see the eye (prospect) cursor.  Regardless of which cursor is showing, if you click on a tile, the explorer moves there and reveals all the adjacent hidden tiles next turn. If the tile is one that can be prospected he will accomplish this at the same time.

Ideally you want to choose tiles for exploration that are adjacent to lots of hidden terrain and could also contain minerals.

Prospecting and exploring both take one turn. Next turn all adjacent terrain tiles will be revealed.  If you find a mineral an icon will be shown in the prospected tile.