A centerfold is the central spread of a magazine, and is usually a fold-out oversize page. This is most often a three-sheet spread where only one half of the center spread folds out, but may be a four-sheet fold-out, or even more.
In common modern usage, the phrase centerfold most commonly refers to the extra-large spread depicting a nude model in the center of an adult magazine. The subject of such a depiction is also commonly referred to as a centerfold, though I would assert that this is a misuse. In addition to nudie-mag depictions, centerfolds are commonly used for nonsexual advertisements.
The Eric Carle children's book Papa, Please Get the Moon for Me makes good use of unconventional fold-outs including a 8-12 (depending on how you count) page centerfold.
Centerfold is also the name of a song and an album by the J. Geils Band. The album was released by Connoisseur Collection on November 12, 1997 and includes:
The song originally appeared on their 1981 Album, Freeze Frame and turned out to be one of their most well known. The lyrics can be seen at many web sites including the third and fourth URLs at the bottom.
Finally, Centerfold is also a romance novel. It is Harlequin Romance, No 2969 by Valerie Parv and was originally published as Centrefold. There are a number of other books around with the word centerfold as a central element of the title.