Margin of error and confidence interval for a sample mean.
It means that if you repeated the same sampling process many times, about 95% of the intervals computed that way would contain the true population mean. It does not mean there's a 95% chance this specific interval contains the true value.
The margin of error includes s / √n, so as n grows, that term shrinks — larger samples give a more precise (narrower) estimate of the mean for the same standard deviation and confidence level.
Higher confidence (e.g. 99% vs 90%) uses a larger z-score, which increases the margin of error. You trade precision (a narrower range) for greater certainty that the interval captures the true mean.