The BFC is simply the land area that a city can eventually work. Other tiles may be within cultural borders, but only the tiles two spaces or less from the city tile (except the diagonals) can be worked by the city's citizens and be productive.
Tiles outside of the BFC can be improved by a settler and any resource exploited there can be accessed if it is connected to the trade network, but there is no production (food, hammers, commerce) gained from such a tile.