Wikipedia has a reasonable entry on Dual Power, and it's worth clicking over to have a look if you want a more thorough historical treatment than I'm prepared to give here.
The tl;dr: "Dual power" was a phrase originally coined by V. I. Lenin during the early days of the Russian Revolution, when the Czar had fallen, but state power was contested between the Soviet worker's councils and the provisional government. Lenin was describing a situation where two different governments, both new and unstable, were building their institutions and power bases in parallel and in opposition to one another; this was a really unusual situation, and what we're facing now bears little similarity to it. More contemporary socialists have used the term to mean, basically, undermining state control by building alternative organizations that provide services and adjudicate conflicts; in a sense, robbing the current state apparatus of market share.
In this sense, Lenin was describing a war, while we're describing an insurgency.
As a strategy of revolution, the idea of Dual Power is that the state derives its power from the legitimacy granted to its structures by the masses of people. All of us, every day, interact with state apparatus, in everything from law enforcement to food stamps to road construction. Because the state administers these things, we confer power and legitimacy on that state when we use them, whether we like it or not. If we can find some way to avoid using these structures, we undermine the power of the state that administers them.
Our ability to simply boycott state structure is pretty limited, but we can, in many situations, set up alternatives. For example, state-run food programs (EBT, TANF, "food stamps") provide a crucial service, but generally involve monitoring, reporting, and snooping into the lives of working class people in need that serve to enforce the power and social dominance of the state. People are, indeed, disempowered by utilizing state aid programs, but it is not, as right wing advocates claim, because such aid disincentivizes work; it's because of the intrusive and humiliation "othering" that those in need suffer at the hands of the state bureaucracy in order to access aid (I speak from experience).
Community-run food banks, on the other hand, provide an alternative source of aid for neighbors in need; fulfilling a service that the state also provides, but doing it in a way that builds rather than undermines community solidarity and pride. The people who receive the aid, and those that give it, belong to the same community, and both have a concrete example of a community solving a problem internally, without relying on a government agency that deliberately cultivates an air of superiority, of distinction, from the community it ostensibly serves.
If this leads to a general realization that the state (in its current form or any form at all) is not necessary for living, that it simply maintains a de facto monopoly on the power to solve problems, a monopoly that can be undermined, we have an instance of Dual Power as a revolutionary act. The Black Panthers' Free Breakfast for School Children program is an excellent historical example of this strategy at work. The Panthers declared that black communities in the United States were not locked in poverty because of a lack of industry or ability on their own part, but because of policies of the state, and they proceeded to prove it by addressing a critical concern, child nutrition, with no resources from the state whatsoever.
So, why am I harping on this so much in a blog about surviving climate change and peak oil? Because Dual Power is a strategy with three distinct advantages in the situation in which we find ourselves:
- It does NOT focus on the seizure of existing power structures (sometimes referred to in brief as "seizing State Power," another turn of phrase of comrade Lenin); as these power structures under capitalism are distinctly unsuited to addressing problems of peak oil and climate change--at least not without so much reworking as to make them essentially new structures.
- It can win incremental victories on a variety of scales; Dual Power builds the components of a resilient and independent community, and those components are nearly as useful individually as they would be as part of a post-capitalist, whole system. Whatever the outcome of the war, every battle won brings real and potentially permanent gains.
- As a strategy, it is ideologically very inclusive. All people need to have in common in order to pursue it together is a shared belief that the current system is inadequate to human needs, and can be replaced with one that is, piece by piece. Communists, socialists, libertarians, anarchists, people of a staggering variety of political outlooks can effectively work on Dual Power projects together.