\[S_p^2=\frac{(n_1 -1) S_1^2 + (n_2 -1) S_2^2 + \dotsc + (n_k -1) S_k^2 }{n_1 + n_2 + \dotsc +n_k - k}\]
where \(S_i^2\) is the sample variance.
It estimates the variance of populations with different means, but the same variance.