The asymptotic variance-covariance matrix displays the variances and covariances of the random terms in the model. The diagonal values are the variances of the terms. The off-diagonal values represent the covariances of any two random terms. Minitab uses the variances to calculate the standard errors for each random term in the model.
Minitab displays the variance-covariance matrix only if you select Variance-covariance matrix of variance component estimates on the Results subdialog.