The word equilibrium refers, among other things, to concepts of game theory. The most well-known equilibrium in game theory is the Nash equilibrium.
Nash equilibria are situations where each player has chosen a strategy and no single player could improve his situation by unilaterally changing strategy while all the other players keep their strategies.
Cabal equilibria are situations where each player has chosen a strategy and no subset of players could simultaneously change behaviour (while those outside that subset keep their strategies) in a way that no player in that subset is worse off and at least one in the subset is better off.
All cabal equilibria are Nash equilibria but not vice versa.