What does the potential energy diagram of a chemical reaction tell you

By looking at the potential energies before and after the reaction, we can tell that the reaction is exothermic (final < initial) or endodermic (final > initial).

Also, the amount of activation energy gives an idea of the external energy required to initiate the reaction (for example, by heating the reactants).
Furthermore, by the same principle, we can also deduce the activation energy for the reverse reaction.

If a catalyst is available, the diagram will show a reduced activation energy, compared to a reaction without catalyst.  However, it will also show that the catalyst does not alter the initial and final energies of the reaction.