[Nereus]

Disclaimer: I've never had a chemistry class in my life. I'm reading a journal article that states the following:

S₂O₃^2- + 2O₂ + H₂O → 2SO₄^2- + 2H⁺

has the standard Gibbs energy of −766 kJ/mol at 25ºC. So, this is energy produced per moles of what?! Reactant? Product? If so, which reactant or product and how do I figure that out? Or does it just mean that if I reacted 1 mole of thiosulfate with 2 moles of oxygen, I'd end up with 766 kJ of energy? Any help would be appreciated!

[Yggdrasil]

Or does it just mean that if I reacted 1 mole of thiosulfate with 2 moles of oxygen, I'd end up with 766 kJ of energy?

Yes, this is the correct interpretation.  If the reaction had been written 2S2O32- + 4O2 + 2H2O --> ... then the ΔG would be -1532 kJ/mol.

[Borek]

So, this is energy produced per moles of what?!

As funny as it sounds - "mole of reaction as written".