A potential energy surface (PES) is a conceptual and mathematical representation of the potential energy of a system, typically in the context of molecular and quantum mechanics. It describes how the potential energy of a system varies with the configuration of its particles, such as the positions of atoms in a molecule.
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A potential energy surface assigns potential energy to the configurations of the reacting chemical atoms, for a specified electronic description. A reaction coordinate selects a path through this many-dimensional configuration space; a potential-energy profile then records the potential energy along that path. Different paths can share endpoints but cross different barriers. See the IUPAC Gold Book: potential-energy reaction surface.