What does this equation mean?

Here $f_i$ is the fraction of time the device spends in power state i (sleep, always-on monitoring, escalated inference, radio) and $P_i$ is the measured — not datasheet-typical — power draw in that state. This formulation is worth writing out because it exposes the one lever that dominates every other design decision: since $f_{\text{sleep}}$ is normally close to one and $P_{\text{sleep}}$ is normally the smallest term, the average power is overwhelmingly sensitive to the escalation rate — how often the cheap monitoring stage decides something interesting is happening — far more than to how efficient the expensive inference stage is once escalated. A system that escalates twice as often as necessary can double its average power even with a perfectly efficient inference core.