The Spider is an example of a centralized organization that is controlled by the brain in the head and can easily be stopped by damaging the head. If you cut off a leg it can limp along but it doesn't get replaced. The starfish on the other hand has no brain. Its five arms are complete in themselves. If you cut one off, the main body grows a replacement and the one arm grows another four so you have 2 starfish.
They describe lots of examples such as the big record companies vs. Napster/Kazaa/edonkey/emule each of which became even more decentralized and harder to stop whereas the big record/media companies couldn't move fast enough to deal with this enemy.
Another example is the Apache vs. the Spanish invaders who were not able to disrupt this strongly distributed organization for a very long period of time as compared to the invasion of Mexico by Cortez who was able to beat the Aztecs (who were also) in no time by tricking Montezuma and then killing him.
Think about the current situation in Iraq. There is no-one in charge of the insurgency. In simplest terms, it is led by many independent people who are angry and take advantage of the chaos that was left because we removed Saddam. Street gangs in US cities are another example.
They talk about enabling workers/participants to do their jobs and take on their own responsibility which results in a very effective mechanism. They gave the classic example of the General Motors factory that was turned into a United Motors factory managed by Toyota in Japanese company style. Using the same workers as before, the productivity and product quality became significantly greater than that produced by the old top-down management style.
I hadn't thought too much about these ideas in these terms in the past but they really do agree with a lot of what I believe. My philosophy as a manager (I was a manager of Multics software development in Honeywell) was to enable the people who worked for me to do their jobs not tell them what to do. I'd often say - think of this in reverse: consider that I work for you and you have to inform me as to what I have to do in order for you to do your job. It usually took me a while to train a new boss when I got one. Yes sometimes things get a bit chaotic but its alot better than the "it's not my job" methodology coupled with "we have to get permission and probably they won't grant it" that causes so many organizations to get in a rut.
In our large centralized organization of a company I'd often see these starfish effects. Several times a new upper manager of Honeywell decided to kill the Multics project but never succeeded. The customers and the developers were in essence a grass roots movement and an amorphous community that ended up turning the whole thing around to allow the project to continue.
You can think of lots of potential examples where rigid organization prevents something from being done. The other day at the City Council meeting the DPW director was explaining that it was too hard to regularly check all the disabled person's ramps from sidewalk to street so it is only done every 5 years. Now, every day Parking Control officers walk down essentially every street in Cambridge either enforcing meter violations or resident parking violations. Why couldn't they report ramp errors? Sorry wrong department. The post office can't remove graffiti from mail boxes rapidly because they have one graffiti remover and he doesn't know where the graffiti is and can't cruise all the streets. Of course everyday each mail box is visited by a postal worker - usually multiple times a day - why can't they report the instances of graffiti?