How does resonance affect the stability of an anion?

[LyahFitzpatrick 2E]

I know this is old material, but how does the resonance of an acid's conjugate anion relate to the acid's strength? Why do resonance structures correlate with stability?

[Stephen_Kim_1D]

Resonance structures delocalize charge so that the negative charge on the anion isn't all located at one atom, and is instead spread throughout the entire molecule. For example, HSO4-, when it's acting as an acid, has the conjugate base of the sulfate anion SO4 2-. If we look at sulfate without resonance, the two oxygens with single bonds to sulfur would have a -1 charge each. These negative charges, if they were located at the oxygens like this, would make the molecule unstable since it can easily react with other atoms. But, SO4 2- does have resonance, since the four S-O bonds are the same length; the -2 total charge is distributed over the four oxygens rather than over just the two oxygens, making it more stable.