In statistical mechanics, a system is in equilibrium if "the probability of finding the system in any one state is independent of time"(Reif, pg 43).
In equilibrium, the macroparameters of the system (such as energy, volume, temperature, etc) are constant. One of the fundamental postulates of statistical mechanics is that "an isolated system in equilibrium is equally likely to be in any of its states" (Reif, pg 43). In soft matter, the concept of equilibrium is fundamental in areas such as self-assembly, because a system tends to go toward its equilibrium state, and once it reaches there, it will stay in equilibrium.
In statistical mechanics there are several techniques for finding the state of a system at equilibrium. Some of the more prominent methods include maximizing entropy S in an isolated system, minimizing energy U in a closed system, minimizing the Helmholtz Free Energy F for a system in thermal equilibrium with a reservoir, and minimizing the Gibbs Free Energy for a system in thermal and pressure equilibrium with a reservoir. The Gibbs Free Energy is used often to find out what will be the spontaneous course of action of a system. In chemical equilibria, this spontaneity is also described by Le Chatelier's Principle: an equilibrium will shift to counter-act change.
Statistical and thermal physics by Federick Reif, 1964 McGraw-Hill,Inc.