Dual Process Theory posits two types of processes in the human brain. According to one characterization, Type 2 (also known as System 2) processes are those which require working memory, and Type 1 (also known as System 1) are those which do not.
The terms System 1 and System 2 were originally coined by the psychologist Keith Stanovich and then popularized by Daniel Kahneman in his book Thinking, Fast and Slow. Stanovich noted that a number of fields within psychology had been developing various kinds of theories distinguishing between fast/intuitive on the one hand and slow/deliberative thinking on the other. Often these fields were not aware of each other. The S1/S2 model was offered as a general version of these specific theories, highlighting features of the two modes of thought that tended to appear in all the theories.
Since then, academics have continued to discuss the models. Among other developments, Stanovich and other authors have discontinued the use of the System 1/System 2 terminology as misleading, choosing to instead talk about Type 1 and Type 2 processing. [...] there’s no single “System 1”: rather, a wide variety of different processes and systems are lumped together under this term. It is also unclear whether there is any single System 2, either. [...]
People sometimes refer to Type 1 reasoning as biased, and to Type 2 reasoning as unbiased. But [...] there is nothing that makes one of the two types intrinsically more or less biased than the other. The bias-correction power of Type 2 processing emerges from the fact that if Type 1 operations are known to be erroneous and a rule-based procedure for correcting them exists, a Type 2 operation can be learned which implements that rule.
-- Kaj Sotala, Against “System 1” and “System 2″