People value intelligence and will apply that label to themselves even if it may not be true. It's a hard thing to measure though IQ does it reasonably well. To those who have a high IQ: what is it like? Can you pick up any book, read it, and understand the gist with minimal repetition? Can you infer solid and accurate conclusions based on a small amount of evidence? Is any subject or discipline up for grabs or do you have to have a keen interest in a particular field in order to flourish? What is something you are able to do that you know is because of your intelligence -- the proverbial 1,000 pound deadlift of the brain, if you will.
There is no point to these questions other than curiosity.
Pattern recognition. Pattern recognition is a key component of intelligence. It's why IQ tests have a lot of 'what number is next in this series' and 'which of these things is not like the other' questions. You are a lot better at predicting outcomes - positive and negative - because you recognize patterns. You see people making the same mistakes repeatedly, and wonder why. It's not that you never make mistakes, but you never make them twice. You are also really good at extrapolating the consequences of others' mistakes, ie: 'johnny stuck a fork in an electrical outlet and got shocked. I'd better not stick a fork in an electrical outlet.'