Underemployment equilibrium describes the state of the economy in which unemployment is consistently higher than usual.
In this state, the economy has reached a macroeconomic equilibrium point somewhere below full potential output, leading to persistent unemployment.
The underemployment equilibrium is a classic part of the Keynesian theory of how a recession can lead to a sustained depression in the economy.
Underemployment itself is a separate term that refers to one of the possible components of unemployment, but is otherwise unrelated to the idea of underemployment equilibrium.