In a so-called "gentleman's magazine," such as Playboy, it would be a photograph of a naked woman. The speaker is complaining that, not only does he have to wait a month for the story to be continued, he doesn't even get to look at a naked woman.
I am used to seeing "centrefold/centerfold" (all one word). A quick Google search finds "center fold" (no discrimination in search terms) 231,000 times, "centre fold" (38,200 times), "centrefold" (188,000 times) and "centerfold" (4,120,000 times). The spelling preference, therefore, appears to be the one-word version. Just thought I'd pass that along.