Math Easy Solutions, O²⁻ means oxygen has gained 2 electrons, so it’s the oxide ion with a net charge of minus two, not a neutral oxygen atom anymore. In compounds, oxygen usually has an oxidation state of −2, which is just chemists’ bookkeeping for electron ownership in bonds, though there are exceptions like peroxides and OF₂ per Chem LibreTexts and Chemguide. In electrolysis, that matters because oxygen-containing ions can be oxidized or reduced depending on the electrode reaction, which is exactly the kind of chemistry your electrolysis thread is poking at.