(Found as part of a wikipedia article on bookbinding)
Most of the following terms apply only with respect to American practices:
A leaf -(often wrongly referred to as a folio) - typically has two pages of text and/or images, front and back, in a finished book. The Latin for leaf is folium, therefore "folio" should be followed by a number to distinguish between recto and verso. Thus "folio 5r" means "on the recto of the leaf numbered 5", although technically not accurate, it is normal to say "on folio 5r". In everyday speech it is common to refer to "turning the pages of a book", although it would be more accurate to say "turning the leaves of a book"; this is the origin of the phrase "to turn over a new leaf" i.e. to start on a fresh blank page.
The recto side - of a leaf faces left when the leaf is held straight up from the spine (in a paginated book this is usually an odd-numbered page).
The verso side - of a leaf faces right when the leaf is held straight up from the spine (in a paginated book this is usually an even-numbered page).
A bifolium - (often wrongly called a "bifolio", "bi-folio", or even "bifold") is a single sheet folded in half to make two leaves. The plural is "bifolia", not "bifolios".
A section - sometimes called a gathering, or, especially if unprinted, a quire, is a group of bifolia nested together as a single unit. In a completed book, each quire is sewn through its fold. Depending of how many bifolia a quire is made of, it could be called:
duernion – two bifolia, producing four leaves;
ternion – three bifolia, producing six leaves;
quaternion – four bifolia, producing eight leaves;
quinternion – five bifolia, producing ten leaves;
sextern or sexternion – six bifolia, producing twelve leaves.
A codex - is a series of one or more quires sewn through their folds, and linked together by the sewing thread.
A signature - in the context of printed books, is a section that contains text. Though the term signature technically refers to the signature mark, traditionally a letter or number printed on the first leaf of a section in order to facilitate collation, the distinction is rarely made today.
Folio, quarto - and so on may also refer to the size of the finished book, based on the size of sheet that an early paper maker could conveniently turn out with a manual press. Paper sizes could vary considerably, and the finished size was also affected by how the pages were trimmed, so the sizes given are rough values only.
A folio volume - is typically 15 in (38 cm) or more in height, the largest sort of regular book.
A quarto volume - is typically about 9 in (23 cm) by 12 in (30 cm), roughly the size of most modern magazines. A sheet folded in quarto (also 4to or 4º) is folded in half twice at right angles to make four leaves. Also called: eight-page signature.
An octavo volume - is typically about 5 to 6 in (13 to 15 cm) by 8 to 9 in (20 to 23 cm), the size of most modern digest magazines or trade paperbacks. A sheet folded in octavo (also 8vo or 8º) is folded in half 3 times to make 8 leaves. Also called: sixteen-page signature.
A sextodecimo volume - is about 4 1⁄2 in (11 cm) by 6 3⁄4 in (17 cm), the size of most mass market paperbacks. A sheet folded in sextodecimo (also 16mo or 16º) is folded in half 4 times to make 16 leaves. Also called: 32-page signature.
Duodecimo - or 12mo, 24mo, 32mo, and even 64mo are other possible sizes. Modern paper mills can produce very large sheets, so a modern printer will often print 64 or 128 pages on a single sheet.
Trimming - separates the leaves of the bound book. A sheet folded in quarto will have folds at the spine and also across the top, so the top folds must be trimmed away before the leaves can be turned. A quire folded in octavo or greater may also require that the other two sides be trimmed. Deckle Edge, or Uncut books are untrimmed or incompletely trimmed, and may be of special interest to book collectors.
Using some of these terms at your next bookclub meeting will make you sound like a smarty mcsmartyson...or a wee bit pretentious. Regardless now you now some of the terms that make up your beloved books :-) Happy Reading Everybody!