What is the justification or scientific theory for the assertion that IQ tests measure intelligence?

The justification is that they identify the abilities that they consider "intelligence".  By selecting easily-measured qualities and excluding all the others, they come up with a number.    Personally, I know lots of people that aren't super high in IQ, but are really smart in different ways.  Many of them are hard to quantify, but very useful.

IQ testing provides a basis of comparison between the individual tested and the population on which the test was standardized. The test assesses performance on a finite number of dimensions. There exists a body of research that relates levels of performance on these dimensions with performance in other areas. The results of IQ testing can be useful in predicting success in other areas of interest. The issue of whether these tests actually measure what we generally mean by intelligence can be debated without undermining the predictive value of the test results.

IQ doesn't seem to have any scientific basis and as far as I can tell no statistical importance outside of studying correlation of changes in groups.  I think though that even with that narrow use it is problematic.

The ability to acquire knowledge and skills is aptitude actually. The ability to think rationally, act purposefully and use available resources effectively is called intelligence! That is the layman sense of definition that you gave there! It is more about how you adjust and succeed in different environments! Like how you adjust to your school life and succeed in that particular environment. Cause let's face it, we all know that being in school doesn't exactly mean innovating anything. It is all about remembering the terms of what you have been taught. It is not about what you can do and discover but what you can learn!

There isn't. They were designed to measure lack of intelligence.  If you fell below a certain point on the scale invented by Albert Binet, you were given extra instruction in school. (You can turn a screw with a coin - that doesn't make a dime a screwdriver.  You can use the Stanford-Binet test to measure intelligence - that doesn't make it a test to measure intelligence.)

I think IQ scores do relate to problem solving skills, abstract and quick thinking. It  teases out education and learning as a separate factor. If you are selecting a general for the battlefield situation, better to have someone with a high IQ (all other factors equal)

has a great answer to this. I'd just like to add that the validity of IQ tests as measuring intelligence is that they are correlated with other measurable outcomes which we believe to be at least partially the result of being smarter - namely, educational achievement and income. IQ scores in childhood/adolescent years have some predictive power for later life outcomes like college graduation, income, and employment. It clearly doesn't explain everything, but it has more predictive power than say, hair color or chin width. So it's not perfect, but not totally useless. It should be noted that other sorts of standardized tests (like the SATs and the http://en.wikipedia.org/wiki/Armed_Services_Vocational_Aptitude_Battery) have similar properties, depending on the test. Of course, you will always find counterexamples, because it's just a statistical relationship. But the general trend is that IQ, income, and education are positively related. The problem with using IQ tests to measure intelligence is that we don't have a well-defined notion of intelligence. So therefore we have no way of knowing how good a numerical proxy IQ scores are, because we have no idea what target we are trying to hit. The only sense of accuracy we can have is how well it predicts other objective outcomes that we define as requiring intelligence.