https://physics.stackexchange.com/quest ... a-universe
The vacuum is "empty" in every precise sense of the word. What we call "particles" in quantum field theory are states created by so-called annihilation and creation operators, which represent "substracting" and "adding" a particle of a certain type to a state. The free vacuum is by definition precisely the state from which you cannnot substract anything, hence it is "empty". The interacting vacuum is by definition the lowest-lying energy state, but we can't talk about particles for interacting states, so it's meaningless to ask if it is "empty".
The "boiling brew of particles" is a misinterpretationg of what so-called vacuum bubbles mean. They are the Feynman diagrams that contribute to the energy of the interacting vacuum state, and if internal lines of such diagrams described actual particles, then these diagrams would mean a continuous creation and annihilation of particles in the vacuum. But the internal lines of Feynman diagrams are not associated to actual particles states (i.e. no creation/annihilation operator of the free theory belongs to them), so this is nonsense. There are no particles in the vacuum and they don't create a universe.
He is misinterpreting Feynman diagrams to give laymen reading the book a magical and mysterious, but math-free picture of what quantum field theory is about. This picture is almost completely wrong.
It's the lowest-lying energy state of the theory, and the start for so-called perturbation theory. Not much more.