Fog of war
Some maps/scenarios limit the information visible to a player. Fog of war (or more simply, fog) limits visibility of units. This can be enabled per-side by the scenario. In addition, a multiplayer game can override the map settings and enable or disable fog for all sides.
When this is enabled, the map begins under a gray haze that obscures all units it covers. Each unit can peer into this haze, pushing back the fog (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 haze removed from them, allowing the unit in that hex (if any) to become visible to the player. Once a hex has been cleared of fog, it remains clear until the end of the side's turn (unless the scenario explicitly causes it to become re-fogged). At the end of a side's turn, if a hex is no longer in the visual range of a unit, it becomes re-fogged. In addition, re-fogging occurs for the defender's side in a combat, if the defending unit is killed. In version 1.10 and earlier, re-fogging can also occur at various times during a side's turn.
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, fog clearing occurs automatically, with one exception: units created by WML after the prestart event will not pierce the haze until they are moved, the side's turn ends, or a [redraw] tag instructs the game to clear fog.
If a player does something that causes a hex to be cleared of fog, that action (and all prior actions) cannot be undone. Players can plot moves without clearing fog by either making use of planning mode or toggling on "delayed shroud updates" (yes, this delays updates for both shroud and fog). The latter is found in the context (right-click) menu when playing the game. When fog updates are delayed, performing a not-undoable action (such as an attack or ending the turn) will cause earlier actions to clear fog. In addition, a player can manually cause earlier actions to clear fog by selecting "update shroud now" (appears in the context menu when fog/shroud updates are delayed).