Stability, in a general sense, refers to how a system responds to being disturbed. Stable systems will resist the disturbance and return to an equilibrium, while unstable systems will amplify the disturbance and either find a new equilibrium or collapse.
Applying this to politics, a place with political stability will resist crises and challenges to the status quo. Even during periods of massive unrest, the government (and society at large) will continue to function. In a place with political instability, crises compound. Small problems can quickly combine and amplify each other and result in the failure of government/society at large.
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