That's his greatest contribution (see Alex on this same point, and Jeff Ely). Let's say you privatize a water system in Africa and write a 30-year contract with a private French company to run the thing. As the contract nears its end, and if renewal is not obvious, the company has an incentive to "asset strip," or at the very least not maintain the value of the pipes. Alternatively, the government might signal, in advance, that it has every intention of renewing the contract. The company then has the incentive to lower quality to consumers, since it expects renewal a and faces weaker competitive constraints.
In other words, franchise bidding, or "ex ante" competition for the market doesn't always resolve monopoly issues The key problem is the existence of a fixed investment in the pipes and that the value of the pipes depends on investments from both the government and the company. It can be hard to write a contract for a good solution, since any allocation of the residual rights creates some distortion or another. This has in fact been a very real problem with privatization around the world in many settings. Oliver Williamson outlined these arguments in his debate with Harold Demsetz over privatizing cable TV. Much of the literature on "mechanism design," such as David Baron's pieces, picks up on this problem and extends Williamson's work.
Williamson is a truly important economist. If you read him, especially in his later work, he also has lots of taxonomy and verbiage. The key is to cut through to the substance, which is plentiful.
Here is John Nye on the Prize.