OFF GRID refers to a power system that generates electricity such as a solar array. The energy produced is stored in batteries and the energy system isn't connected to the utility power grid.

ON GRID refers to a energy power system that's connected to the utility power grid. In the case of a solar energy system, excess power from the solar array, not used by the home/business is fed into the utility grid and the utility meter records the power excess as a credit. This excess is then used when solar power is not available. Batteries aren't needed in a on grid system.