The following blog post from Rob Hopkins is by far the best explanation of what Transition Towns is about. It contains numerous but implicit references to chaos theory: that we have to self-organize, start from the simplest level, from the ground up, that we don't know the mature state of the system or even where we're going, but that by following simple 'nearest neighbor' rules, we can create resilient communities and perhaps arrive at a mature system state that is resilient and more ecologically sound than the current one.
After reading this, my 'aha' moment was that I realized that there's no way we can solve the problem of global climate change—it's impossible. It's too big, it's too complex and too intractable. Since we can't solve the problem of global climate change (or 'peak oil') we have to focus on problems that we can solve. "Focus on possibilities, not probabilities." We have the capacity to build local, resilient communities that can survive whatever hits us, whether climate change, peak oil, economic collapse, or the decline of an empire. But just working on any collective social problem won't help us develop the right skills for the crisis. In order to develop the necessary skills to survive climate change, we have to work on problems and projects that "model" the larger crisis. So working on the cooperative local provision of food, shelter, energy and governance in a low carbon mode, creating systems that can react quickly and flexibly to localized change, helps us develop capacities for a future that is energy scarce and climate disrupted. We can solve those problems by working through movements like Transition Towns that ask the right questions and focus on the right issues, even if they don't have all the answers. "Resilience" doesn't solve the problem of climate change either—it just helps us to survive it so that we can adapt to whatever conditions will be thrust upon us for the indefinite future. In the face of these insurmountable dilemmas, we cannot avoid collapse, large or small. Catastrophic transformation is on it's way and we can't stop it. All we can do is survive it and hope that the new communities we create will evolve into a system that is adapted to the new world that awaits us.