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.

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.

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 6, 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.

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. Sometimes a single (evade) 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 least a removal spell.