The Banished Zone, known as the Removed from Play Zone or the Removed Zone prior to the PSCT update, is a semi-official term used to refer to the location where your banished Cards are being placed.
Not actually a Zone
The Banished Zone is not actually a zone, and as such, it is not included on official playmats. Instead of using the term "Banished Zone", Card texts directly refer to "Cards that are banished" or "the player's banished Cards" (previously "the player's Removed from Play Cards" or "the player's Cards that are removed from play").
Banished Cards are left face-up unless an Effect specifically banishes them face-down. Cards that are banished face-down are not public knowledge and can only be looked at by their owner.