Some maps/scenarios limit the information visible to a player. Shroud limits visibility of terrain. This can be enabled per-side by the scenario. In addition, a multiplayer game can override the map settings and enable or disable shroud for all sides.
When this is enabled, the map begins as uniform blackness that obscures everything it covers. Each unit can peer into this blackness, pushing back the shroud (for its side) as far as it can move in one turn, plus one hex. That is, each unit can see every hex it could attack next turn if it were to end its turn in its current location. (This is not entirely accurate for slowed units, unless one assumes the unit is re-slowed before its next turn.) Hexes that can be seen have the blackness removed from them, allowing the terrain to become visible to the player. Once a hex has been cleared of shroud, it remains clear unless the scenario explicitly causes it to become re-shrouded.
Some units might have a vision range and terrain costs that are different than their movement range and costs. There is not yet a way to tell if this is the case other than trying it out and seeing what happens. So far, the only mainline use of this feature is to allow elves in Under the Burning Suns to see across deep water.
For the most part, shroud clearing occurs automatically, with one exception: units created by WML after the prestart event will not pierce the darkness until they are moved, the side's turn ends, or a [redraw] tag instructs the game to clear shroud.
If a player does something that causes a hex to be cleared of shroud, that action (and all prior actions) cannot be undone. Players can plot moves without clearing shroud by either making use of planning mode or toggling on "delayed shroud updates". The latter is found in the context (right-click) menu when playing the game. When shroud updates are delayed, performing a not-undoable action (such as an attack or ending the turn) will cause earlier actions to clear the shroud. In addition, a player can manually cause earlier actions to clear the shroud by selecting "update shroud now" (appears in the context menu when shroud updates are delayed).