The Banished Zone, known as the Removed from Play Zone prior to the PSCT update, is a semi-official term used to refer to the location where a player's banished cards are placed. It has also been referred to as the banished pile, or the removed from play pile (sometimes formatted as removed-from-play pile) prior to the PSCT update. It is not actually a Zone, and as such, does not exist on any game mats. Card texts that would refer to this 'Zone' instead directly refer to "cards that are banished" or "the player's banished cards" rather than cards that are in a specific Zone.
Cards in the Banished Zone are left face-up, unless an effect specifically banishes them face-down. Neither player may look at a card that is banished face-down. However, in the OCG, cards that are banished face-down may be checked, if necessary, for verification for certain card effects.
Most Duelists (and most video games) place the Banished Zone either to the right of the Graveyard or above the Graveyard's Zone (above or to the right of the "3" in the image at top). The artwork of one particular card, "Chain Material", explicitly shows an example of where banished cards may be placed.