If you have never been in a film with Kevin Bacon, but have been in a film with someone who has been in a film with Kevin Bacon, you have a Bacon number of two, and so on. This goes for random networks, or random graphs. However, we know that a lot of local clustering occurs. The caveman knew only his nearest neighbors, who also knew only their nearest neighbors. It is very likely that a lot of our closest friends are also our friends' closest friends.
Most real networks are somewhere between the two extremes of randomness and order.
We have some local connections, as in the ring model, but also some distant acquaintances. Duncan Watts's claim to fame is the introduction of a small number of random shortcuts into the ring model, which he described in a recent Nature paper he coauthored with Steve Strogatz of Cornell University. By tuning this number, one produces a phase transition, or rather a smooth crossover, between the small world represented by the random network and the large world represented by the lattice. This is, roughly, the content of Watt's book. A rather unrelated and quite uninspired chapter on cellular automata and coevolutionary games is tagged on.