Critical values of $t$ are specific scores that mark the boundaries of the most extreme portions of the $t$ distribution for a given alpha level and degrees of freedom. For example, the two-tailed critical values when there are $24$ degrees of freedom and $\alpha$ is $.05$ are $2.064$ and $-2.064$. If a calculated $t$ score falls beyond a critical value in either direction, it is in the extreme tail of the distribution, leading to the rejection of the null hypothesis.