I'm currently learning about substitution and elimination reactions and to do so I need to learn about bases and nucleophiles.

Apparently a good base is an unstable species.

What does stability even mean in chemistry?

I just need to conceptually understand and wrap my head around this concept of a compound or atom or species being 'stable' or 'unstable'. Please don't explain it in complicated terms.

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    $\begingroup$ Thinking about something as being 'stable' or 'unstable' is often misleading as stability can depend on many things. Esters, for instance, may be perfectly 'stable' if left out in a vial, but incredibly unstable if stirred in a flask with some aqueous base. Stability should, therefore, always be qualified, for instance thermodynamic stability and kinetic stability are both terms often considered by chemists. $\endgroup$ – NotEvans. Nov 12 '15 at 23:54
  • $\begingroup$ And to take @NotNicolaou’s comment a step further, kinetic ‘stability’ should not be called ‘stability’ at all but better inertness. $\endgroup$ – Jan Dec 25 '15 at 22:37

Stability has several meanings. A compound can be stable on its own, under the given conditions such as temperature and pressure. This is the case for a lot of compounds. The other definition of stable could be a compound's inability to react with other molecules (like the inability of carboxylic acids to be oxidized). This is probably what you meant. A good base, like $R-O^-$ is unstable because of the +I effect of the alkyl group, which shifts the electron density towards oxygen, which in turn makes the ion a very good and strong nucleophile. This is the reason why such "good bases" tend to cause eliminations and substitutions in organic molecules.

P.S.: This is the simplest explanation I can provide. If you have any doubts, ask them in the comments.

P.S.S.: Stability of a compound can also be explained on the basis of what @NotNicolaou said.

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