Stability refers to the ability to remain in a certain state.
The "state" in some instances can be dynamic, and in other
instances it can't.
Stability in chemistry refers to elements or compounds that not
reactive (don't "want" to continue combining with other elements to
acheive stability). The Noble gases Ne, He, Ar, etc. are very
stable. While some elements and compounds are
stable at STP (standard temperature and pressure) others are
not, yet they may be stable at high pressure and low temperature
for example. Everything might be deemed "stable" at absolute zero
in a chemical sense. The equilibrium state of a controlled chemical
reaction would be stable even though chances would still occur at a
certain rate.
Stability in a physical sense is an object's ability to remain
in a certain position without movement.
There is financial stability, emotional stability, economic
stability, environmental stability, genetic stability...all are
dynamic systems that change within a certain set of parameters (so
unstable in the strictest sense) but are stable in a broad, overall
sense as long as they remain/perform within certain guidelines.