A homogeneity hypothesis test formally tests if the populations have equal variances.
Many statistical hypothesis tests and estimators of effect size assume that the variances of the populations are equal. This assumption allows the variances of each group to be pooled together to provide a better estimate of the population variance. A better estimate of the variance increases the statistical power of the test meaning you can use a smaller sample size to detect the same difference, or detect smaller differences and make sharper inferences with the same sample size.
When the test p-value is small, you can reject the null hypothesis and conclude that the populations differ in variance.
