The condition when Variances are equal/constant across groups or Populations. This is a common assumption in many statistical tests involving two or more distributions. Also called homoskedasicity. The converse (when Variances are unequal) is called heteroskedasticity.
Several tests are available to help evaluate the assumption of homogeneity of two or more Variances, among them:
1. F-Ratio test for two Variances - requires normality of the populations
2. Levene's Modified test (also called Brown-Forsythe test) for more than two Variances - does not require normality of the populations
3. Bartlett's test for more than two Variances - requires normality of the populations
More on tests of Homogeneity of Variances from NIST: - http://www.itl.nist.gov/div898/handbook/eda/section3/eda359.htm