Board presence denotes the collection of permanents a particular player controls in play.
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.
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.
You are being beaten down by some threats you can't handle, and you need an answer fast.