State value under a policy

Defines how valuable a state is when future actions are selected by policy pi.

V sub pi of s equals the expected return G at time t, under policy pi, given that the state at time t is s.

The value of state s is the average return you should expect after arriving there and continuing with policy pi.

The expectation is the main verb: average future returns over uncertainty while holding the current state fixed.

This is a definition, not an update rule. A paper may later introduce Bellman equations or estimators for calculating it.