Old English bord "a plank, flat surface," from Proto-Germanic *burdam (cf. Old Norse borð "plank," Dutch bord "board," Gothic fotu-baurd "foot-stool," German Brett "plank"), from PIE *bhrdh- "board," from root *bherdh- "to cut." See also board (n.2), with which this is so confused as practically to form one word (if indeed they were not the same word all along).
A board is thinner than a plank, and generally less than 2.5 inches thick. The transferred meaning "food" (late 14c.) is an extension of the late Old English sense of "table" (cf. boarder, boarding); hence, also, above board "honest, open" (1610s). A further extension is to "table where council is held" (1570s), then transferred to "leadership council, council (that meets at a table)," 1610s.