“Folio” and “quarto” refer to the number of times a sheet of paper has been folded for printing, and thus gives a rough indication of the size of the book.
A folio is a book for which the initial sheet of paper has been folded in half, providing two leaves and four pages (the front and back of each leaf) for printing.
A quarto is folded again, giving four leaves and eight pages.
To learn about folios and quartos firsthand, visit the Folger’s DIY First Folio and DIY Quarto interactive tutorials.