Laurie and Jim, I think what you have is one of the old predecessors to Masonite/hard board. I'm not really sure how it was made but you used to see it often on ceilings and kitchen walls. It is real similar to the stuff that they used to sell as "pressed leather" chair seat bottoms. The stuff came prepainted (usually in awful colors) and was meant to be glued on the wall.
Back then, hide glue was pretty common also and heat will soften that pretty easily but still leave a glue mess. Hot water might help in removing that after the board has been removed. But you don't want to leave water on the wall any longer than necessary either or it will soak in and degrade the plaster.
Wish I could tell you more but I have to go paint the cat. Lucy is still in pretty good shape but I don't like the color. LOL