What is IQ?
Francis Galton seems to have been the first to systematically attempt to measure intelligence, but the tests he devised were failures. Alfred Binet wasn't actually trying to measure intelligence - he called what he measured "mental age" - but the mainly verbal tests he devised to measure educational readiness became the first IQ tests. (See the Wikipedia article: Intelligence Quotient for this and much else.
Unlike Galton's attempts, these tests turned out to have large correlations with educational achievement and performance on a lot of tasks that required planning and thinking. Moveover, a wide variety of related tests correlated strongly with each other, leading to Spearman's hypothesis that there must be some underlying factor 'g' (for general intelligence) that underlay them all. That was the origin of the idea that such tests, subsequently called IQ tests, in fact measured intelligence.
So what do IQ tests measure? 114 years after Binet's invention we still have very little idea. Its role can be compared to the role of entropy in physics after Carnot and Clausius but before Maxwell, Boltzmann and Gibbs. We know it measures something important, and we can measure it, but we only have the faintest idea what it means.
It's important because it's a good predictor of a bunch of skills important in an industrial and technological society: learning, planning, solving related problems, prediction of behavior, and it's easy to measure.
IQ test questions usually call on the test taker to make inferences about relationships. These inferences can be verbal, geometric, or, as in Raven's progressive matrices, abstractly geometric. Spearman's point about a 'g' factor was that the results of various kinds of tests tend to be correlated. Binet thought instead that there were a number of different intellectual faculties which had a certain degree of independence. There is support for both ideas, in that verbal and mathematical abilities, for example, are frequently correlated, but there are many exceptions, some of them dramatic.
IQ denialists love to point out that Feynman reputedly score 'only' 124 on an IQ test he took in elementary school. 124 is a bit less than two standard deviations above the norm, but everybody (OK, all physics nerds) know that he was really really smart. The idea that this in some way means IQ tests are bogus would be laughable if so many didn't take it seriously. Of course any such test, especially of elementary school kids, can be wrong. Perhaps it was primarily a verbal test, when we have independent evidence that while Feynman was a math prodigy, his performance in other subjects was frequently quite modest.
IQ tests are pervasive. If you want to join the Army, work for Walmart, go to college, or play pro football you are going to take some tests that are essentially IQ tests. If you want to work for an elite tech company like Google or Facebook, you will be subjected to some questioning that among other things, amounts to a test of elite IQ.
These tests are not just fads. They are given because they help recruiters decide whether they are wasting their money hiring you or assigning you a job or a place in their freshman class.
There is hardly any trait of the brain that is more fundamental than its plasticity, its tendency to be altered by experience. Does that apply to IQ? Almost certainly, but both the nature and amount of alteration are at best controversial, as are the kinds of influences that make a difference, except, of course, that it is well known that disease, malnutrition, and other insults to the body also affect the brain and IQ.
Perhaps the most vexing question about IQ is the existence of national and racial differences. IQ tests and proxies for IQ tests consistently show such differences. This gives tremendous aid and comfort to racists of all flavors, even though whites do not come out on top of the rankings - except for Ashkenazi Jews, who do. Chinese are next. Furious wars are fought over the reasons for the differences, but the evidence is ambiguous. It's virtually certain that at least some of the differences are due to cultural, nutritional, and environmental differences, but it really isn't known how much.
James Watson, one of the most accomplished scientists of the Twentieth Century, was recently burned at the stake by the forces of PC at what used to be his own lab for declining to recant his opinion that the differences were genetic. William Connolley* recently reminded us of the dictum of Heraclitus "ἦθος ἀνθρώπῳ δαίμων," usually translated as "character is fate." Honest Jim was always a character, and his, or at least his honesty, caught up with him in the end.
I tend to disagree, and not just because I don't want to be consigned to the flames. I think that we just don't know enough about IQ for intelligent answers to exist. A recent study found, for example, that offering monetary rewards for higher scores consistently increased IQ scores, and the more money offered, the more scores improved.