O is a singular oxygen atom. O2 is a molecule made of two oxygen molecules. Our atmosphere is made of mostly O2, which our bodies have evolved to breathe. We breathe in O2 and cellular respiration requires it (C6H12O6+6O2→6CO2+6H2O).
O is oxygen, while O2 is dioxygen.
Examples of other oxygen molecules are: 03 which is ozone (trioxygen), there's O4 that is metastable and is actaully made up of two O2 molecules (tetraoxygen), and O8 which is a form of pressurised solid O2 (when you freeze O2 to below around 55 Kelvin and pressurise to around 10 GPa (1.45e+6 psi)it becomes known as ε oxygen or red oxygen due to the color changing from blue to red).