Well, how should you measure a bow's length? Is it the un-strung length as the crow flies, do you follow the curve of the limbs, should it be strung?
AMO stands for the Archery Manufacturers Organization. It created a set of standards for things such as defining bow length. When people give a length of a bow in inches they almost always mean AMO bow length. AMO bow length is the length of the string plus 3 inches. So a 66 inch AMO bow is supposed to take a 63 inch string. But, some people sell strings by "AMO" length rather than actual length, so your AMO 66 inch bow takes an AMO 66 inch string (actual length 63 inches). And, not all bows take a string exactly 3 inches less than the printed bow length. And some bows, especially English Longbows, are measured at their un-strung length.