A method of Variational inference where the space of distributions over which we optimize the variational distribution is distributions where the individual parameters are independent. This is known as a mean field approximation (as we ignore statistical dependences).

See here

In the above we show what the optimal $q_i(w_i)$ is, when only optimizing $q_i$ and keeping the rest of $q_j$ fixed. This is a Coordinate descent update. So if this update is easy to calculate, we can use coordinate descent to optimize the mean field ELBO