The short answer is that IQ is what IQ tests measure. That answer is saved from total circularity by the fact that there is a high correlation between results of a bunch of different tests of reasoning. Typical IQ tests have questions designed to test short term memory, general knowledge, ability to follow written or spoken instructions, and ability to reason concretely and abstractly, ability to generalize and analyze relationships as well as speed of mental processing. Early intelligence researchers noticed that there was a strong correlation among the results of rather different tests and the statistician and psychologist Spearman hypothesized that the correlation was due to an underlying g-factor, the g standing for general intelligence.
A century or so later, our knowledge of the underlying biological substrate of IQ has made only limited progress. We know of lots of genetic and environmental factors that limit IQ, but have only vague indications of what things produce higher IQs. For example, our big human brains seem to be necessary for high IQ, and bigger brains are associated with higher IQs among people. Higher IQ children's brains, according to MRI studies, develop a bit differently than those of lower IQ children.
So why should we care about something so little understood? Because IQ tests are ubiquitous and effective predictors of a wide variety of life outcomes. Moreover they are easy and cheap to administer. If you want to work at Walmart or play in the NFL you will probably take the Wonderlic, a short IQ test. This testing is not due to any kind of superstition but by the fact that these organizations have found strong correlations between performance and test scores. NFL IQs, on average, are about equal to the average of the population as a whole, but if you want to play quarterback or offensive line, you better be about 2/3 of a standard deviation above the norm. If you can tackle, cover the pass, and are hella fast, you can probably play cornerback even if you are a standard deviation below.