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You can think of Gibbs free energy as the energy level of reactants/products. If you think of a reaction curve where the reactants sit at a certain G and the products sit at another G, the difference between those energies will be delta G. If the reactants G are lower than products G then it will require energy to perform the reaction.
As many have said above, Free Energy is the amount of energy available from a reaction or a process that can be used to do work. Delta G is change in this free energy, and Delta G naught is this value at equilibrium and standard conditions.
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