A Magic: The Gathering control deck is a type of deck or archetype that focuses on dominating the game using some or all of the following kinds of strategies: long term card advantage, resource denial, permission, and inevitability. Control decks are based around efficiency and controlling the board, which is where the name comes from. Control decks have been prominent throughout the history of Magic, and by design of the game, will always be, to varying degrees of success.
Control decks generally have some combination or all of these features or strategies: card advantage, permission, resource denial, and inevitability. Though these features are not limited to only control decks, they are features that are commonly thought of when speaking about a control deck.
Card advantage refers to the term of having access to more cards than the opponent. To gain card advantage, one must trade advantageously against an opponent. For example, if a player casts a Terminate on an opponent creature that has an enchantment attached to it, the player has traded one card for two of the opponent's. This exchange can be called a "two for one" for short.
Two main ways control decks gain card advantage are board "sweepers" and card drawing. Because most decks in Magic try to win through creature damage, during most portions of a game, the aggressive or midrange deck will have more than one creature on the board. The control deck takes advantage of this and uses board sweeping spells, or "wraths", such as Day of Judgement, to destroy multiple opponent creatures while only expending one card. By trading this way multiple times throughout the game, the control deck gains significant card advantage since it will have only used two to four cards to trade for an opponent's five to ten cards. The other major way control decks gain card advantage is through card drawing spells. These are generally used in the later portions of the game due to the fact that card drawing spells do not affect the board state. Card drawing spells range from Divination, a net gain of one card, to Stroke of Genius, a spell that can provide tens of cards worth of card advantage. By repeatedly casting card drawing spells throughout the game, the control deck can gain huge amounts of long term card advantage over the opponent.