"side of ship," Old English bord "border, rim, ship's side," from Proto-Germanic *burdan (source also of Old Frisian bord, Old Saxon bord, Dutch boord "border, edge, ship's side," German Bord "margin, border," Old High German bart, Old Norse barð "margin, shore, ship-board"), perhaps from the same source as board (n.1), but not all sources accept this. Connected to border; see also starboard.
If not etymologically related to board (n.1), the two forms represented in English by these words were nonetheless confused at an early date in most Germanic languages, a situation made worse in English because this Germanic word also was adopted in Medieval Latin as bordus (source of Italian and Spanish bordo) and entered Old French as bort "beam, board, plank; side of a ship" (12c., Modern French bord), via either Medieval Latin or Frankish, and from thence it came over with the Normans to mingle with its native cousins. By now the senses are inextricably tangled. Some etymology dictionaries treat them as having been the same word all along.
To go by the board originally was "fall overboard" (1757), of a mast, etc., hence, generally, "be completely lost or destroyed" (1835). To be on board is from c. 1500, originally nautical, "close alongside;" then, less technically, "on the ship" (1708), perhaps by influence of aboard, or from the noun in the sense "plank;" extended to trains, planes, general situations.