They measure a specific type or aspect of intelligence. The breadth of aspects of intelligence they can measure is limited, because by their very nature they can only test intelligence applied to problems where there is exactly one possible answer (at least out of the options), and it's objectively correct, no room for subjective assessment. (What I'm referring to is multiple choice questions.)

In practice, I notice that they seem to favor formal, analytic thinking and the ability to solve puzzles. And people with extremely high IQs also tend to be very clever, so that's probably another thing they measure (or maybe there's some extent to which that aspect of intelligence is just positively correlated with aspects IQ tests measure).

While what they can or do measure is limited in scope, it's an important aspect of intelligence, especially for purposes society tends to highly esteem--academics, science, STEM (IQ is highly correlated with academic success)--and it's also known that all aspects of intelligence are positively correlated with each other, so a person with high IQ is likely to have high intelligence in general, that is, in all the ways we really mean when we say someone is intelligent.

So, it irritates me when people say IQ is meaningless, because (a) they just assume this without understanding the subject at all, (b) it's just one-sided hyperbole, taking something that has some truth to it and making it into a polar absolute, and absolutist thinking is a common problem, (b) they can't see the obvious, (c) they're wrong and being wrong always seems malignant to me for whatever reason, (d) it's just a self-serving cope for the fact that they don't score high in intelligence tests, yet they value high intelligence (as is the social norm) and they don't want to feel humiliated or devalued, and (c) it makes them fail to honor high intelligence where it's due because they refuse to recognize it. (And this isn't about "I have a high IQ, honor me," I'm not that weak, I'm talking about the value of recognizing everyone with a high IQ everywhere.)

I have a fascination with people with extremely high IQs. I love to talk with them, and to be known by them. I used to regularly talk with people with IQs over 180, I miss those days. I've also talked with the person who held the Guinness world record for the highest IQ (196, IIRC), Chris Langan (though the high IQ community in general doesn't like him, and they say he only scored that high because he took the test 3 different names and his real IQ is likely closer to his first score, 170, though that's still extremely high.)

As for my IQ, my scores vary. I used to take online IQ tests, and I usually scored between 135 and 145. I took the WAIS-III once, but I was very out of it that day. I think my overall IQ was measured at 120, while one subscore, which I think was called "functional IQ," was measured at 138. I've taken the MENSA practice test and passed it. I took one IQ test in my life that I paid for, which was a normalized test (meaning they statistically adjusted the results so that they fit the bell curve, and it also took into account test takers' results from other tests, so the results are reliable), and got 146. It was the Logima Strictica 36, which was specifically designed to test creativity (insofar as you can possibly do that with the multiple choice format). I once took a German test that was only composed of questions where you look at sequences of grids with dots in them and choose the next in the sequence, and I got 160. IIRC, it seemed to be all about tracking the linear motions of individual dots across the sequences, despite the fact that multiple dots would frequently take up the same cell (in which case only one dot was displayed) as they moved along. The lowest I ever scored was 98. It was a test that ran in DOS (the text-based OS prior to Windows), which was ridiculously hard and relied on a lot of obscure knowledge. I haven't taken an IQ test in many years, and I'm probably less good at taking IQ tests nowadays because I seem to have lost some of my ability to think about certain logical constructs or to formulate plans of attack in solving certain kinds of conceptual problems. It's like on a preconceptual level I can no longer choose a single direction to take and try to take them all simultaneously. (It's a case of "The person who chases two rabbits catches neither.)