Community cards are face-up cards that everyone in the poker game shares, and are allowed to use in order to make their best possible hand.
In Hold'em and Omaha the five board cards that are dealt out as the flop (three cards), the turn (fourth card, also known as fourth street), and the river (fifth and last card, also known as fifth street) comprise the community cards. In Omaha
players are only allowed to use three community cards when they build their hand, and they must use two of their own cards.
In Hold'em there are no restrictions on how to use the community cards. In fact, you could end up playing all five community cards and none of your own cards, in which case you are said to be "playing the board". This often occurs when the community cards make up a five-card straight or a full house.