To model portfolio losses, such as when an investor holds positions in a collection of linear or primary assets with different volatilities, a univariate loss model becomes inadequate and instead a multivariate framework is needed. First recall the univariate loss model
$$l_t = \sigma_t z_t $$
indexed by $t$ as the asset volatility $\sigma$ varies with time. In a portfolio, the losses arise from the net sum of losses and gains of the portfolio’s constituent assests. These losses may be assumed to be identically distributed for each asset in the portfolio but they are not necssarily independent. The independence of one assets volatility from another asset’s volatility is not likely even if it happens momentarily and so there is not much sense in building a model that makes that assumption.
Therefore in order to model the dependence between pairs of assets, we build a matrix of volatilities of all the assets in the portfolio and the co-dependent relationship between them. There are two possible properties of each asset pair that we could use to model their mutual dependence. One is the covariance, the other is the correlation.