Dictionary Definition:

“A thermodynamic quantity equal to the enthalpy (of a system or process) minus the product of the entropy and the absolute temperature.”

Selected from OxfordDictionaries.com

Functional Definition:

Gibbs free energy is the amount of energy available to do work in a systems at constant temperature and pressure. Gibbs free energy ( ΔG) can describe the spontaneity of a reaction. If  ΔG is negative then the reaction is spontaneous. If  ΔG is positive then the reaction is not spontaneous and it requires an imput of nergy from outside the reaction.

Gibbs free energy is the relationship of all three key thermodynamic properties described in chemistry and biology; Gibbs free energy, enthalpy, and entropy. Gibbs free energy is equal to enthalpy minus temperature (in kelvin) times entropy.  Overall it is the relationship of heat into a system,  the absolute temperature of the system, and the randomness of the system.