In an ANOVA, the term Mean Square refers to an estimate of the population variance based on the variability among a given set of measures.

In a one way ANOVA, the Within Mean Square is an estimate of the population variance based on the average of all s²s within the several samples.

In a one way ANOVA the Between Mean Square is an estimate of the population variance based on the s² of the sample means multiplied by n (the size of the samples).