According to this chapter, this transition (the development of writing) was accomplished through the needs of civilization and government. Developing a writing system is difficult. People need to solve a wide variety of problems when creating a full system of writing. This is really not necessary for hunter-gatherer societies so they do not spend the resources needed to do so. But civilizations can benefit from writing. This starts out with the need for governments to keep track of things like tax revenues or what they have in their storehouses and it goes from there.
Thus, the transition to written communication occurs through a long process (described early in the chapter) that is based on the needs of bureaucratic civilizations.