Not an answer, but it must be formatted in a way that a comment cannot hold.

If you continue reading, the author defines this notation:

Here, $\langle \cdot \rangle_q$ means the expectation or mean under the density $q$ and $D(\cdot\ ||\ \cdot)$ is the cross-entropy or Kullback-Leibler divergence between the two densities.

I have taken liberties to embed links to the relevant Wikipedia articles in the quote