Question

oh,the affair was quite above board .explain

Answer 1

There is pun intended in the above lines. He tries to convince Lavinia, his wife that he had a pretty legitimate realtionship with Helen. Also he tells Lavinia that all the situations between him and Lavinia were above the board, ie there was no cheating.

Answer 2

Actually this sentence has 2 meanings. One talks about the affair and flirtations between John and Laura Hinkle. John assures his wife that the whole affair with Laura was only limited to the time when both of them were working the Ouija Board, i.e. it all happened across the Ouija Board and there is no reason for Lavinia to suspect anything.
The other relationship is the one between John and the ghost, Helen. 'Above board' means that the whole relationship was perfectly normal, correct and proper. There were no bad intentions from either side.