The Archery Manufacterors Organization started in the '60's. It sets the standards for all archery equipment. At that time there was no such thing as a compound bow.
The AMO on the side of a bow usually stands for the string length. In a recurve, that is usually about 3" shorter than the actual length of the bow limbs from notch to notch measured along the belly of th bow; the side of the bow facing the archer when held in shooting position.
The standard weight indication is **# @ 28" (** being the draw expressed numerically) such as 50# @ 28"
or 37# @ 26", however the bow is marked.
Later, when compound bows hit the market the AMO standards applied.
One extra thing AMO states for compounds is the speed rating of the bow, usually rated as speed with a 30" arrow drawn 28", with a 450 grain arrow as the standard.
IBO speed rating is different in that they do not specify an arrow lenght but do specify a certain number of grain weight per inch of arrow, because many compounds use overdraws with shorter arrows. The IBO speed rating of a bow is usually a lot faster than the AMO rating.
I may get thrown off of the Traditional Forum for talking about IBO and compounds, but I felt it was justified to explain the difference between AMO and IBO.
Jack is correct, in that the AMO standard is 3". It was (correct me if I'm wrong there PAPA) designated as such "back in the day". Usually in regards to an endless loop string provided with your new bow. (i.e. a 60" bow came with a giant looped endless string that measured 57" when it was made).
When these "standards" were set, you shot what you shot. Endless loop for a production bow was the order of the day. Now, with tuning so prevalent with traditional archers, custom is.
The "norm" now is generally -3" for a longbow, and -4" for a recurve. Preferably an adjustable string such as a flemish for tuning purposes. (yes...they had them in the 'olden days' also.....)
So...to answer...AMO is a guide....not a rule (anymore)....but if you give me a 57" string for a 60" recurve, I'm gonna throw it back in your face...and make myself a 56" flemish twist.