Critical value

A critical value marks how far out on a distribution you go to capture a chosen probability. For a confidence interval it is the number of standard errors that brackets the middle C% of the sampling distribution. For example, a 95% confidence interval for a mean using the normal model uses $z^* = 1.96$, because 95% of the standard normal curve lies within 1.96 standard deviations of the center. With small samples and unknown population spread you instead read $t^*$ from the $t$-distribution using the degrees of freedom.