The gravitational energy term is the rate at which energy is released by changes of gravitational potential energy. i.e. the $\epsilon$ terms are rates of change of energy. For instance, if a star contracts, this releases gravitational potential energy that adds to the power generated by nuclear fusion.

In a main sequence star, the "gravitational energy" term is close to zero because the star changes in size very slowly and basically all the luminosity is provided by nuclear fusion.

In the phase of evolution discussed in your quote, the core expands and the gravitational potential energy becomes less negative. This requires energy and so in the terminology of Carroll & Ostlie, the "gravitational energy term" becomes negative and the luminosity, which must be equal to the nuclear energy and gravitational energy terms, will fall.

The gravitational energy term is the rate at which energy is released by changes of gravitational potential energy. i.e. the $\epsilon$ terms are rates of change of energy. For instance, if a star contracts, this releases gravitational potential energy that adds to the power generated by nuclear fusion.

In a main sequence star, the "gravitational energy" term is close to zero because the star changes in size very slowly and basically all the luminosity is provided by nuclear fusion.

In the phase of evolution discussed in your quote, the core expands and the gravitational potential energy becomes less negative. This requires energy and so in the terminology of Carroll & Ostlie, the "gravitational energy term" becomes negative and the luminosity, which must be equal to the sum of the nuclear energy and gravitational energy terms, will fall.