In model-based clustering the mixture component distributions are most commonly assumed to be multivariate normal, with component-specific mean vectors and covariance matrices, although other mixture distributions can also be used within this framework (Banfield & Raftery, 1993). Focusing on the case of multivariate normal mixtures, the parameters of the model are the within-cluster mean vectors and covariance matrices. Consider plotting two variables X and Y. The group means determine where on the X and Y axes the data cloud (or scatter) is located, and the covariance between X and Y determines the orientation, shape and volume of the cloud. Extending this to more than two variables, the group-specific means determine the location of each of the clusters, and the covariance matrices contain the information concerning the orientation, shape and volume of the data cloud for each cluster.
