A one-line summary:

rise->complexity->exponential rise in resource consumption->running out of resources->fragmentation->decline.

A summary from two amazon reviews:

Tainter first elegantly disposes of the usual theories of social decline (disappearance of natural resources, invasions of barbarians, etc). He then lays out his theory of decline: as societies become more complex, the costs of meeting new challenges increase, until there comes a point where extra resources devoted to meeting new challenges produce diminishsing and then negative returns. At this point, societies become less complex (they collapse into smaller societies). For Tainter, social problems are always (ultimately) a problem of recruiting enough energy to "fuel" the increasing social complexity which is necessary to solve ever-newer problems.

Tainter argues that human societies exist to solve problems. He looks at a score of societal collapses, focusing on three: Rome, the Maya, and the Chacoan Indians of the American Southwest. As these societies solved problems - food production, security, public works - they became increasingly complex. Complexity however carries with it overhead costs, e.g. administration, maintaining an army, tax collection, infrastructure maintenance, etc. As the society confronts new problems additional complexity is required to solve them. Eventually a point is reached where the overhead costs that are generated result in diminishing returns in terms of effectiveness. The society wastefully expends its resources trying to maintain its bloated condition until it finally collapses into smaller, simpler, more efficient units.