I first heard of this concept through Daniel Kahneman’s bestsellerfrom 2011. This has come under fire recently in light of the replicability crisis in psychology (see here).
The first version of this ‘pop science’ idea seems to have been proposed, and more seriously studied, by Evans (1984). As this author explains in his most recent book (Evans, 2019):
In terms of quantity, the analytic system can meet very little of the cognitive demands on the brain, but in terms of quality it can do things that the heuristic system cannot. The analytic system is required when we need to decontextualize problems and examine their formal structure; it is involved whenever we engage in hypothetical thinking, supposition or mental simulation; it is also needed when we apply explicitly learnt rules. By contrast the heuristic system is massively parallel and rapid, and its strength lies in identifying relevant prior knowledge and belief that are then activated and made available for conscious processing.