Re: Rationality is the ability to do well on hard decision problems.
That sounds like the definition of intelligence - though it skips the "range of problems" bit. The "range of problems" qualification seems to be doing useful and desirable work there - though do we really want two separate terms meaning practically the same thing?
Certainly rationality as defined here is within the fuzzy cloud of groundings of the rather vague word "intelligence". However, it is probably closer in meaning to "wisdom".
Rationality differs from intelligence as commonly used in that intelligence in humans is commonly judged on abstract problems in situations of certainty, such as IQ tests, and frequently involves comparative assesments (IQ, exams) under time pressure and with tuition and preparation. Rationality typically deals with real-world problems with all the open-endedness that entails, in situations of uncertainty and without tuition or practice.
This article is an attempt to summarize basic material, and thus probably won't have anything new for the experienced crowd.
Related: 11 Core Rationalist Skills, What is Bayesianism?
Less Wrong is a blog devoted to refining the art of human rationality, but what is rationality? Rationality is unlike any subject I studied at school or university, and it is probably the case that the synthesis of subjects and ideas here on Less Wrong is fairly unique.
Fundamentally, rationality is the study of general methods for good decision-making, especially where the decision is hard to get right. When an individual is considering whether to get a cryonics policy, or when a country is trying to work out what to do about global warming, one is within the realm of decision-making that we can use rationality to improve. People do badly on hard decision problems for a variety of reasons, including: that they are not born with the ability to deal with the scientific knowledge and complex systems that our modern world runs on, that they haven't been warned that they should think critically about their own reasoning, that they belong to groups that collectively hold faulty beliefs, and that their emotions and biases skew their reasoning process.
Another central theme of rationality is truth-seeking. Truth-seeking is often used as an aid to decision-making: if you're trying to decide whether to get a cryonics policy, you might want to find out whether the technology has any good evidence suggesting that it might work. We can make good decisions by getting an accurate estimate of the relevant facts and parameters, and then choosing the best option according to our understanding of things; if our understanding is more accurate, this will tend to work better.
Often, the processes of truth-seeking and decision-making, both on the individual level and the group level are subject to biases: systematic failures to get to the truth or to make good decisions. Biases in individual humans are an extremely serious problem - most people make important life-decisions without even realizing the extent and severity of the cognitive biases they were born with. Therefore rational thought requires a good deal of critical thinking - analyzing and reflecting on your own thought processes in order to iron out the many flaws they contain. Group dynamics can introduce mechanisms of irrationality above and beyond the individual biases and failings of members of the group, and often good decision-making in groups is most severely hampered by flawed social epistemology. An acute example of this phenomenon is The Pope telling HIV infested Africa to stop using condoms; a social phenomenon (religion) was responsible for a failure to make good decisions.
Perhaps the best way to understand rationality is to see some techniques that are used, and some examples of its use.
Rationality techniques and topics include: