Alphabet soup refers to the abbreviations of the various sanctioning bodies that have proliferated since the 1980s, and their handing out of what many boxing aficianados consider "cheap" world titles.
Once upon a time there were only eight weight divisions, with only one champion per division, for a total of eight boxing world champions at any one time (sometimes fewer, if one boxer was the champion of two or more divisions at a time). A contender became the world champion only by beating the then-World Champion, or by beating other contenders in an elimination tournament for a vacant world title. In those days there were only a handful of world sanctioning bodies--including the National Boxing Association, New York State Athletic Commission, International Boxing Union, British Boxing Board of Control, and a few others.
Then, from the 1980s onward, many new boxing sanctioning bodies arose, to the point where it seemed that if the manager or promoter paid the requisite sanctioning fee, his boxer could fight for a somewhat dubious "world title," although the boxer's record may not be what was generally considered by most fans and commentators as "world-class." (Currently there are 17 weight divisions and some six major sanctioning organizations, for a total of 102 world champions. This figure could be doubled to almost 200 when one adds in world titles labeled as "interim," silver, diamond, emeritus, in recess, or something similar.) Thus, some boxing fans and critics belittle these "world championships" by labeling them "alphabet soup" titles or trinkets.