Confidence Interval Estimation (CIE)

How do you understand CIE?

We use sample mean Xbar Margin of Error to estimate population mean. We can only say that we are 90, 95, or even 99% confidence that the population mean is somewhere within the interval;

We use sample proportion Pbar Margin of Error to estimate population proportion. We can only say that we are 90, 95, or even 99% confidence that the population proportion is somewhere within the interval;

Does that mean Population mean or proportion changes or moves or varies?

How do you understand this?