A page is a closed half-plane. A book is a collection of pages identified along the boundary of the half-planes. This common boundary is called the spine .
Books provide another topological space in which to embed graphs.
Every graph embeds in a book with three pages, so it is common to put some restrictions on how the graph is drawn. Specifically, we require that all vertices lie on the spine and no edge contains a point on the spine other than its ends. They also give the construction achieving this upper bound. I do not know why he was interested in these graphs or if any work has been done on the problem.