The simplest green energy definition would be energy produced from energy sources that are environmentally more friendly (or "greener") compared to fossil fuels (coal, oil, and natural gas). Green energy therefore includes all renewable energy sources (solar, wind, geothermal, biofuels, hydropower), and by definition should also include nuclear energy though there are many environmentalists who oppose the idea of talking about nuclear energy as the green energy because of the nuclear waste issue, and its harmful environmental effects.
Green energy term was coined to separate highly polluting fossil fuels from other less polluting, environmentally friendlier energy options such as renewable energy sources. Climate change has become a global threat, and world needs to find cleaner (less emitting) energy options, and thus the importance of green energy keeps growing.
Green energy is still not powerful enough to compete with fossil fuels. This is mostly because green energy is still significantly more expensive energy option compared to fossil fuels, and thus many countries, especially developing ones, rather stick with cheaper fossil fuels such as coal.
It also has to be said that term green energy doesn't include only renewable energy sources but can in more broader term also include the conservation of energy (for instance a green energy example is also a building constructed in a way that it keeps itself cool in the daytime and heated in the night through its architectural design instead of relying on air-conditioning or a heating system).
The promotion of green energy does not only include using more renewable energy sources in years to come but also to make currently dominant fossil fuels energy technologies more greener and less polluting (such as clean coal technologies).
Term green energy is sometimes identified with the term sustainable energy but this is not entirely correct because sustainable energy also includes technologies that improve energy efficiency. Green energy doesn't refer to efficiency of renewable energy sources but is only interested in their positive environmental impact (compared to fossil fuels).