What are our brains doing when they are (supposedly) doing nothing?

Pezullo et al. address the question of this post's title in an article in Trends in Cognitive Sciences: "The secret life of predictive brains: what's spontaneous activity for?" (motivated readers can obtain a PDF of the article by emailing me). They suggest an explanation for why brains are constantly active, displaying sophisticated dynamical patterns of spontaneous activity, even when not engaging in tasks or receiving external sensory stimuli. I pass on the article highlights and summary: 

Spontaneous brain dynamics are manifestations of top-down dynamics of generative models detached from action–perception cycles. 

Generative models constantly produce top-down dynamics, but we call them expectations and attention during task engagement and spontaneous activity at rest. 

Spontaneous brain dynamics during resting periods optimize generative models for future interactions by maximizing the entropy of explanations in the absence of specific data and reducing model complexity. 

Low-frequency brain fluctuations during spontaneous activity reflect transitions between generic priors consisting of low-dimensional representations and connectivity patterns of the most frequent behavioral states. 

High-frequency fluctuations during spontaneous activity in the hippocampus and other regions may support generative replay and model learning.

Brains at rest generate dynamical activity that is highly structured in space and time. We suggest that spontaneous activity, as in rest or dreaming, underlies top-down dynamics of generative models. During active tasks, generative models provide top-down predictive signals for perception, cognition, and action. When the brain is at rest and stimuli are weak or absent, top-down dynamics optimize the generative models for future interactions by maximizing the entropy of explanations and minimizing model complexity. Spontaneous fluctuations of correlated activity within and across brain regions may reflect transitions between ‘generic priors’ of the generative model: low dimensional latent variables and connectivity patterns of the most common perceptual, motor, cognitive, and interoceptive states. Even at rest, brains are proactive and predictive.