Face down

Two cards (Illusionary Mask and Ixidron), the morph and megamorph abilities, and the manifest keyword action allow spells and permanents to be face down. A face-down permanent is a 2/2 creature with no text, no name, no subtypes, no expansion symbol, and no mana cost or color indicator (consequently, it is also colorless).

Turning a face-down permanent face up is a special action that can be done any time the player has priority (in other words, any time he or she could cast an instant), but it doesn't use the stack and can't be responded to (in this way, it is similar to playing a land). To do this, it must either have morph or megamorph (and its controller pays its morph cost), or it is a manifested creature card (and its controller pays its mana cost). A token, or a card that is already face up (such as a Clone copying a face down creature), can't be turned face up. If the face-down creature has any counters on it, those remain on the face-up permanent. It's not a new object, and it doesn't enter the battlefield just by turning face up. Any Auras or Equipment attached to it remain attached to it after it turns face up. There are three enchantments in Fate Reforged that manifest a card and then become an Aura attached to it.

Face down (together with its opposite, face up) is part of a permanent's status. Permanents have their own status, which is not a copiable value. Consequently, a copy of a face-down creature will be a face-up 2/2 creature with no characteristics except any that the copy effect gives it (e.g. Cryptoplasm). Since it's face up, such a copy can't be turned face up, unlike the object it's a copy of.

Cards may additionally be face down in other zones. This is the default for the library, but some effects also exile a card face down, and the cards in the special decks in the command zone for Planechase and Archenemy are also usually face down. None of these situations has any correlation with the "face down" status of a permanent.

Rules

Exiled face down

From the Comprehensive Rules (June 7, 2024—Modern Horizons 3)

• 406.3. Exiled cards are, by default, kept face up and may be examined by any player at any time. Cards “exiled face down” can’t be examined by any player except when instructions allow it. However, if a player is instructed to look at a card and then exile it face down, or once a player is allowed to look at a card exiled face down, that player may continue to look at that card until it leaves the exile zone or is part of a pile of cards that are shuffled, even if the instruction allowing the player to do so no longer applies.
  • 406.3a A card exiled face down has no characteristics, but the spell or ability that exiled it may allow it to be played from exile. Unless that card is being cast face down (see rule 708.4), the card is turned face up just before the player announces that they are playing the card (see rule 601.2).
  • 406.3b Some spells and abilities allow a player to cast spells with certain qualities from among face-down cards in exile. A player may cast such a spell only if they are allowed to look at the face-down card in exile and if the resulting spell has the specified qualities.