Unconscious Thought Theory (UTT) refers to the idea that that people may be able to 'work through' complex problems without necessarily paying conscious attention.

Many will have had the experience of waking in the morning with a solution to a problem that had previously proved difficult or impossible to resolve using conscious thought. A similar phenomenon is when someone has a 'Eureka' moment when not consciously concentrating on a problem.

These types of occurrence do not currently have an agreed explanation.

A 2004 research project published in the Journal of Personality and Social Psychology, found that :

Unconscious thought improved the quality of decisions. When people were faced with complex decisions, a few minutes of distraction during which people could engage in unconscious thought - but not in conscious thought - led to superior decisions compared with circumstances under which people could not engage in unconscious thought or to circumstances under which people engaged in conscious thought.
Moreover, a few minutes of conscious thought generally did not lead to better decisions compared with conditions where people did not consciously think. The relative inferiority of conscious thought was expected to be the consequence of the low processing capacity of consciousness."

Source : Journal of Personality and Social Psychology, 87(5), 586–598 ^{[ paywalled ]}

Subsequent research projects, however, have not been able to reproduce similar results, and some psychologists now reject the notion of UTT in its entirety. (example papers : [1] and [2])

Nevertheless, there are still countless anecdotal examples of problem-solving (and also artistic creativity) which appear to be somehow outside the normal realm of conscious thought.(ref.)

Also see : Automaticity a.k.a. 'Autopilot'plugin-autotooltip__plain plugin-autotooltip_bigAutomaticity a.k.a. 'Autopilot'

Most people who routinely drive to and from their workplace will have experienced 'Highway hypnosis' (ref.) at some stage. In other words, arriving at their destination with little or no recollection of the drive.

Leading to the idea that either :