The term board came from the old BBS (late 80s-mid90s) term which stood for bulletin board system. You used a modem to dial in to a server where other local users were dialed in to and you could chat with them or download files.
Although the internet existed, it wasnt being used in a commercial sense as it is now and BBS (bulletin board systems)
http://en.wikipedia.org/wiki/Bulletin_board_system
, bulletin boards ruled the day. So board is an older term for a forum basically.