Assume you have found a set of risk premium factors $F$. Empirically, these factor premiums share a substantial cross-correlation among each other, which creates numerical instabilities and ambiguous interpretations. We orthogonalize them (a.k.a. rotate $F$ to $G$) such that no information is lost and each risk factor premium has:
$$ G := \left(\text{chol}(\Sigma_F)\right)^{-1} \, \times \, \left(F - E[F]\right), $$
where $chol(\Sigma_F)$ is the lower triangular Cholesky decomposition of the covariance matrix $\Sigma_F$ and $G$ is called the 'Gram-Schmidt orthogonalization of $F$'.