Laymen's terms...
A GP Acme is held to a tolerance pertaining to the pitch dia... The faces of the thread are what takes the load, and only the faces. (Major and minor are usually held to like .01 plus/minus thread depth per side, giving .02 +/- tolerances on the major and minor dia) Once that PD starts to wear, nothing stops it but the major or minor diameters, which then begin to wear.
In a Centralized Acme, you hold the major, minor, AND pitch dia to a tight tolerance, giving the screw "more" contact (and load resistance)on 3 surfaces instead of just the PD.
Contact on 3 surfaces rather than just one, is mostly beneficial where the screw and nut will get regular use... all day,every day. A long screw (only supported on the ends)or a bent one, will quickly wear through a pitch dia in a nut, and "slop" or "backlash" will be created. If that is undesirable, use a centralized acme.
Think of the lead screws and nuts in your machines.