A value from the null distribution that is compared with the test statistic value to help decide whether or not to reject the null hypothesis. This value is based on the alpha or significance level of the test. Depending on whether the alternative hypothesis is one or two-sided, there may be one or two Critical Values for the test. It is also called the critical value. The cut-off value(s) define the rejection region for the null hypothesis, so that if the test statistic falls within this region, the null hypothesis is rejected in favor of the alternative.
Consider the test of a null hypothesis that the mean equals a specified value vs. the alternative that it is greater. Let's say the data have a normal distribution under the null hypothesis. Then, for a 5% significance level the cut-off value for the test is the 95th standard normal percentile, 1.645. We will reject the null hypothesis if the test statistic exceeds this cut-off.