This one is an example of American terminology being more old-fashioned and quaint than British: an unusual situation, in this business at least.  In Britain the weight of paper is given as grams per square meter (gsm) which is a usable, simple number.

Over here, basis weight is the weight in pounds of a ream of paper cut to a given standard size for that type of paper.  For book paper the standard size is 25” x 38”.  A ream is defined by the OED as “a quantity of paper, properly 20 quires or 480 sheets, but frequently 500 or more, to allow for waste; of paper for printing, 21½ quires or 516 sheets (a printers’ ream)”.  Let’s not worry about quires and printer’s reams: we down-to-earth Americans define the ream as 500 sheets, so a 50# paper (# standing for basis weight) will clock in at 50lbs if you put 500 sheets, size 25″ x 38″ on a scale.  This is of course not very useful information: who has 500 sheets in that strange size lying around?

It all goes back to ancient times, at least 100 years ago, when many American printing presses would accommodate a 25” x 38” sheet, yielding a 6⅛” x 9¼” book. Because common, this size became the standard.

Basis weight is relevant merely because that’s how paper is sold.  If you want to make any use of the number, you really need the M weight, which tells you how much 1000 sheets in the size you are using will weigh.  This enables you to work out how many pounds of paper you’ll need.  M weight is calculated as follows:

M weight = Length of sheet x Width of sheet x Basis weight divided by 475.

Of course this is only interesting if you ever do sheetfed printing.  For those who deal overseas you can convert from Basis Weight to gsm by dividing the Basis Weight by 0.67565.  To go the other way, multiply the gsm by the same magic number.  But do remember these formulae apply only to book papers: other types of papers have different basis weights.