Board

The Board in Magic: the Gathering is the collection of permanents currently on the battlefield. Each player has their own "board" and the word also describes the battlefield as a whole.

Board presence

Board presence denotes the collection of permanents a particular player controls in play. Lands are considered trivial to count in most matchups but when a control deck is one of the players their access to mana is part of assessing their board presence.

Board state

The board state is the current situation or state of a game. Almost all of the games in Limited will be decided by board state. There are essentially zero strategies in Limited where you can ignore the board. In Constructed, there are decks that can simply "goldfish" (play your deck, ignoring your opponent's actions) their way to victory. Control decks also ignore the board, in that they do not attempt to develop their own.

There are four recognizable board states.

Opening or Developing

Both players are playing cards from their opening hands and establishing themselves as the aggressor or the control player. This is the early part of the game, and one that is critical to how the rest of the game will play out. Typically runs until something around turn 5, barring mana issues on either side. This is the expected turn when both players finish making consistent land drops and have the resources to cast any given spell in their deck. This is also usually the point where players can cast more than one spell a turn, and the player who can leverage the tempo swing is likely to be on the winning side.

Parity

Both players have played most or all of the spells from their hands, but neither has been able to establish a dominating board position. It's a stalemate, with the top of the deck providing the only fuel available to both players. When both players have more than three creatures, it becomes a board stall, as the best attacker on either side can be dogpiled by defenders. Sometimes a single evasive threat may be able to attack, but the clock is far too slow to expect to win with.

Winning

You have more creatures able to attack and evade the creatures of the opponent. If nothing changes, you win the game in a couple of turns.

Losing

Your creatures are unable to profitably block and attacking is irrelevant. A player losing on board will need something high-impact to recover, at the least a removal spell.

Board wipe

At higher rarities, a class of spells can remove multiple creatures from the board, often from both sides. This is a dramatic shift in position as it turns the game into who draws better or has resources left in hand. The potency may vary, for example Pyroclasm, which can be made asymmetrical relatively easily, contrasting with Hour of Devastation, which is more difficult to have a resistant board state.