In a word: yes, they're accurate (with caveats).

There are statistical measures of whether or not someone is in a high percentile, etc. You can calculcate how many standard deviations one person is away from the norm (median), among other ways. Those seem to be somewhat accurate because if statistically speaking, someone scores better than the median, that means they're above average.

Do they mean anything? I don't think they have much of an independent meaning. Who decided that such a test was the best way to measure people's ability or aptitude on a certain topic?

I hate exams like the SAT, etc. Luckily I didn't have to take the GRE to get into graduate school. I think test-making is a racket, to be 100% honest. It's a complete scam put on by College Board or whatever they're called.