Please note that this name is a misnomer, as it is not an actual zone; the term "banished" is used to describe the state of the card.
The Banished Zone, also known as the banished pile and formerly known as the Removed from Play Zone or Removed from Play Pile, holds a player's banished cards. Such cards are left face-up, unless removed by the effect of "Esper Girl", "Lightforce Sword", "Different Dimension Capsule", or "Phantom Hand". Neither player may look at a card that is banished face-down.
While not explicitly mentioned on playmats, the Banished Zone is typically placed by Duelists (and in various video games) above or to the right of their respective Graveyards or in between the field and player. The Yu-Gi-Oh! GX anime often shows Duelists utilizing their pockets as a Banished Zone due to the lack of any place on a Duel Disk to put them.
A "Banished Zone" does not currently exist on Official Gamemats.