Something that is bistable can be resting in two states. In physics, for an ensemble of particles, the bistability comes from the fact that its free energy has three critical points. Two of them are minima and the last is a maximum. By mathematical arguments, the maximum must lie between the two minima. By default, the system state will be in either of the minima states, because that corresponds to the state of lowest energy. The maximum can be visualised as a barrier.
A transition from one state of minimal free energy requires some form of activation energy to penetrate the barrier (compare activation energy and Arrhenius equation for the chemical case.) After the barrier has been reached, the system will relax into the next state of lowest energy again. The time it takes is usually attributed the relaxation time. (There might be uncertainty as to which state will be the new one, but it is often well defined in the situation.)
Optical bistability is an attribute of certain optical devices where two resonant transmissions states are possible and stable, dependent on the input.