I don't have a copy of the story, but based on bits and pieces I read about it online, I'm guessing that this is said by John to his wife, while the ghost, Helen, is in the room, which is why he doesn't want his wife to focus her gaze behind him, where Helen is. " With respect to "board," John works for a lumber company and the main activity in the story has to do with Ouija boards. The Ouija boards indicate that John has had an "affair" with a woman named Helen.
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Here above board is pun .
1John mean to say he is honest and legal
2supposed love affair