Score (verb) - a crease in a sheet of heavyweight paper to facilitate folding.
Why is this important? If you are printing on thick stock, scoring will help prevent cracking. Cracking occurs along the fold as small white paper fibers appear and look as if the inked image is tearing apart at the spine.
Think in 4's. While a printer can do a number of varying folds, in most cases only page counts divisible by 4 will work when the printed product must stitch. This is not a rule and there are exceptions to this (in fact our own web press is capable of folding an 18 page signature). However on most standard stitched books, page counts divisible by 4 are a must.
Signature (noun) - in printing and binding, the name given to a printed sheet after it has been folded.
Why is this important? The more signatures you have, the more costs are involved. If you print a 32 page booklet and the printer is capable of fitting up to 16 total front and back pages on one large sheet of paper, your booklet would have a total of 2 signatures (one for each press sheet comprised of 16 pages). Each press sheet/signature needs plates, paper, ink and finishing services. Anything you do to reduce the total number of signatures (not necessarily pages) will save you big money.