The Map Revealer removes the fog of war from every tile and adds line of sight to every tile for player 1 only.
Civilization 3 .SAV files store the data for fog of war and line of sight in bitmaps in the tile section. So revealing the map simply requires setting all of both of these values from 0 to 1 for every tile for player 1.
As a countermeasure to cheating, if the map revealer is run, in addition to the map being revealed for player 1, the bottomright-most corner of the map will have its fog of war removed for every player. This way, other players can check that tile to be sure that no one's pulling a fast one.