If each player has chosen a strategy and no player can benefit by changing his or her strategy while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitute a Nash equilibrium.
A system may have many possible Nash equilibriums. There is no guarantee that a Nash equilibrium is optimal for the system as a whole. Most are not. However, it is often very difficult to move from one Nash equilibrium to another. To do it successfully, all players must be made aware that a better state is attainable and they must trust each other to change.
Nash equilibriums are named after John F. Nash Jr., whose life was depicted in the movie A Beautiful Mind.