basically it says that, the enthalpy change of a reaction depends only on the initial and final conditions of the reactants and products respectively. the reaction route or reaction pathway has no effect on the enthalpy change.
a quick example is when you produce CO2 from Carbon and oxygen. there are two possible routes:
1) burn C directly in oxygen.
2) burn Carbon to carbon monoxide, and then burn that carbon monoxide to carbon dioxide
but both have the same enthalpy according to Hess' law