What really clicked confidence intervals for me is the explanation that the '90%' in a 90% confidence interval indicates that 90% of the 90% confidence interval

What really clicked confidence intervals for me is the explanation that the '90%' in a 90% confidence interval indicates that 90% of the 90% confidence intervals will contain their true parameter. There is no reason to restrict this to repeating the same experiment many times. The confidence interval above applies to any & all constructed confidence intervals, even those estimating completely unrelated parameters. Relevant xkcd: https://xkcd.com/882/ https://xkcd.com/882/