An Equilibrium is a rest-point or -state of a mathematical system in which values of the system in this point’s vicinity will tend to it (stable equilibrium) or distance themselves from the point. (unstable equilibrium)
Francis Chen’s Definition of an Equilibrium
An equilibrium is a state in which all the forces are balanced, so that a time-independent solution is possible. The equilibrium is stable or unstable according to whether small perturbations are damped or amplified.
There also exist equilibria, that, when pushed across a certain threshold fall out of their current state of stability.