Since I say I am a "cognitive scientist of markets," I damned well better have an answer to what this means.
It's not quite behavioral economics, so let's use the similarities and differences as a starting point. Behavioral economics is a field that grew out of, and as a reaction to, mainstream neoclassical economics. If you flip through a graduate microeconomics textbook, you'll learn from page 1 about various odd assumptions (or axioms) that theorists use. They assume things like perfect information, perfect rationality, infinitely many competitors, purely selfish motives, and so on. These do not sound like real humans, and these real humans do not seem to live in a real market. Although economic theory has its uses, it is riddled with false assumptions.
Behavioral economics is a reaction to neoclassical economics in that it seeks to test – and it often falsifies – these assumptions, particularly those concerning rationality. At the same time, because it is still rooted in the neoclassical tradition, much of behavioral economics uses the same formalisms as neoclassical theory while attempting to introduce more realistic axioms. The most sophisticated uses of behavioral economics (such as some work in behavioral finance) use these more realistic axioms to build new models of these new, more realistic agents and see how they behave under various conditions.
There's nothing wrong with any of this, except that I am not particularly interested in the behavior of axiomatized agents, even if some of the axioms are realistic. I am a scientist and I am interested in actual things – in this case, people and markets. To the extent that formalisms help us to understand these things – which indeed they can at times – then this is all for the good. But too much of modern economics, of both the neoclassical and the behavioral varieties, smells suspiciously like a game for clever people.
The cognitive science of markets is not behavioral economics – it is cognitive science! It is the study of the minds of the individuals who participate in market activities, using cross-disciplinary approaches (such as psychology, neuroscience, anthropology, philosophy, and, yes, economics), but relying especially on rigorous experimentation. It is not particularly concerned with whether its findings can be incorporated into improved axiomatizations of economic agents (that's a business for others), and it is relatively more interested in the underlying psychological mechanisms. Like behavioral economics, though, I believe that the cognitive science of markets has a powerful role to play in explaining the complex patterns that emerge from the activities of individual agents. It incorporates insights from other disciplines (such as consumer psychology, political psychology, and social psychology) that are not generally considered a part of behavioral economics, and by considering the full contexts in which human beings are situated, I believe its explanations can be fuller and more powerful compared to other approaches.
The coming years will see an explosion in this kind of work, I predict, and it has already started (though never under this name). The behavioral revolution in economics was of inestimable importance for changing the way that the discipline thinks about rationality and selfishness, and indeed many of its results are now widely accepted in the profession. If we cognitive scientists educate ourselves in economic matters, we can play a leading role in the next revolution.