Merit badges have their roots in the fact that Scouting was originally designed to indoctrinate boys towards later military service.
Thus, there was an effort to create a reward system for learning new skills, analogous to that found in most militaries.
As was noted in other writeups, several of the merit badges are silly and useless, and there are a number of arts and crafts badges with only 2 to 5 requirements, along the lines of "make a basket". However, the list of badges required for Eagle is composed of those skills judged necessary for a "graduate" of Scouting. From http://www.scouting.org:
In addition, a Scout has a choice between Emergency Preparedness and Lifesaving, and a choice among Cycling, Hiking, and Swimming.
One of the first things that a Scout does after joining is to earn a few badges that he knows intimately and can breeze through the requirements for. In my case, these were Computers, Art, and Reading. Later, once a Scout arrives at camp and needs to show off to his friends, he earns Rifle Shooting and attempts Shotgun Shooting. Later on he might branch out and try something like Wilderness Survival or even Aviation.
The practical upshot of this is that any boy who follows the path laid out by the Boy Scouts of America towards earning his Eagle badge is at the very least learning a number of skills which may help to develop later interests, allow him to save a life, or provide him with a sense of civic duty, and in the best case will give him a method for approaching new skills and challenges that he will benefit from for the rest of his life.