A reaction profile shows the energy change between the reactants and the products. This reaction change can be either positive or negative, and when the enthalpy change is negative the reaction is exothermic whereas when it is positive the reaction is endothermic.
The activation energy is the energy needed for a reaction to initiate, to break bonds in order to create new interactions. The higher the activation energy the higher the energy needed for a reaction to take place, no matter how kinetic favourable the product could be.
Diamonds and Graphite
One prime example where the Gibb’s Free Energy shows that the reaction should proceed is the change of diamonds into graphite. The reason why this does not happen is simply that the high activation energy is high enough for the reaction not to be initiated.