As an European, I did never have any IQ test, nor I know anybody who (to my knowledge) was ever administered an IQ test. I looked at some fac-simile IQ tests on the internet, expecially Raven's matrices.
When I began to read online blogs from the United States, I started to see references to the concept of IQ. I am very confused by the fact that the IQ score seems to be treated as a stable, intrinsic charachteristic of an individual (like the height or the visual acuity).
When you costantly practice some task, you usually become better at that task. I imagine that there exists a finite number of ideas required to solve Raven matrices: even when someone invents new Raven matrices for making new IQ tests, he will do so by remixing the ideas used for previous Raven matrices, because -as Cardano said- "there is practically no new idea which one may bring forward".
The IQ score is the result of an exam, much like school grades. But it is generally understood that school grades are influenced by how much effort you put in the preparation for the exam, by how much your family cares for your grades, and so on. I expect school grades to be fairly correlated to income, or to other mesures of "success".
In a hypothetical society in which all children had to learn chess, and being bad at chess was regarded as a shame, I guess that the ELO chess ratings of 17 year olds would be highly correlated with later achievements. Are IQ tests the only exception to the rule that your grade in an exam is influenced by how much you prepare for that exam? Is there a sense in which IQ is a more "intrinsic" quantity than, for example, the AP exam score, or the ELO chess rating?
Raven's matrices are only one example of an IQ test. Performance across a wide range of domains, from pattern recognition to sensory discrimination to knowledge to reaction time is correlated. This widespread pattern of correlations is likely due to the performance on these many domains sharing causes, with the broadly shared causes being called g.
Since g affects your performance on tests, IQ tests to an extent measure g. However, as you point out, you can often just practice a test to become better. This practice will only make you better at that specific test, though; training your pattern recognition skill with matrices will not make you better at distinguishing the weights and colors of objects using your senses. That is, practice doesn't change your g, but instead improves the test-specific skills called s.
Your IQ score is a combination of g and s factors (and other factors too). And it doesn't even exist unless you take an IQ test. So it can't be a stable innate characteristic of an individual. But g - that is, whatever underlies performance across wildly different tests - must exist independently of the tests, as a characteristic of the individual, and empirically it appears reasonably stable in adulthood, and highly genetic.