Frequentist statistics is a little counter-intuitive. Let’s say you take a sample and compute the sample mean as some value k. Suppose you assume in this case that the value follows a normal distribution, and to simplify things, let’s assume that somehow you knew the standard deviation.
You look at all the possible normal distributions with the particular standard deviation and mean x. Choose those values of x for which the sample mean k falls with 95% range in an interval centered at x. You could then say that there is a 95% confidence interval for a particular range of x. Suppose x fell between k – d and k+d. You could say that there was a 95% confidence interval value of k +/- d.
if what you were sampling was a percentage value, like percentage of proteins in a person’s diet. Then k and d would be percentage values, so you could say something like, there is a 95% confidence interval that the percentage of proteins is 25% +/- 3%
The important thing to notice is that you are choosing the probability distributions to match the result. Bayesian statisticians don’t care for this approach. They might say that it is like a farmer trying to figure out how a pig escaped from its pen and deciding that the pig must have had wings, because then the chances of escape would be 100%.