In poker games where communal gaming is the mode of play, the entire crop of cards at play is what poker players refer to as the board. Examples of board games are flop games like up cards in a 7-Card Stud, Omaha and Hold'em. The players who use board style play are those who don't use any of their hole cards to play. All the cards in play within the community which include turn, flop and river cards put together are jointly referred to as the board. Those cards that are spread out, faced up on the table and are common to each player's hand is part of the board.
If you happen to play with, or watch poker players do their thing, you will hear exclamations such as "Not a single heart was on the board." If it's referring to the cards of a poker player that are faced up in a game like 7-Card Stud, a player may say "His board is a toothless bulldog that can't bite me, so I'll move in on him with another bet." For a community of face-up cards, anyone may say "Why not begin with a flush draw? you can do this unless you've got 4 more diamonds up on the board so you would have to fold."