Finding an adequate definition for clean energy isn't an easy thing to do, mostly because of the issue with nuclear power categorization. While some energy experts believe that nuclear power should be also categorized as a clean energy source because harnessing nuclear energy doesn't emit harmful greenhouse gas emissions others say that nuclear power shouldn't be considered as a clean energy source because of radioactive nuclear waste.
What does this "clean" mean? The clean means environmentally friendly, or given our current energy situation, environmentally more acceptable compared to fossil fuels. This somewhat explains why there is such a big debate whether we should include nuclear power among clean energy sources or not, as energy experts first need to agree whether nuclear power is environmentally more friendly option compared to fossil fuels.
The question about nuclear power categorization is really a question of setting up the limit for term "clean". If clean energy refers only to energy sources that are not connected with greenhouse gas emissions then nuclear power should be considered as one of the clean energy options, and if clean refers to energy sources that are not hazardous for environment then nuclear power cannot be categorized as a clean energy source.
Renewable energy is clean energy and renewable energy sources are clean energy sources because they are considered to be environmentally friendly. However, environmentally friendly isn't the same as perfect, and there is no such thing as perfect energy source. Renewable energy sources can also create environmental damage, for instance harnessing wind power can be connected with noise and visual pollution, harnessing solar power can lead to water shortages, and geothermal drilling can lead to release of many harmful gases.
Fossil fuels (coal, oil and natural gas), are usually referred to as "dirty" energy sources because of the damage they do to our environment, and our planet in general. Fossil fuels, when burn release harmful greenhouse gases, mostly in form of carbon dioxide (CO2) which accelerate the climate change impact. Unlike renewable energy sources which can in certain situations cause some environmental damage fossil fuel burning always causes environmental damage.
Clean energy is not only needed to save the world from the climate change but also to ensure energy security for years to come. Fossil fuels will eventually become depleted, and once this happens world needs to have another solution ready, and clean energy certainly looks like the best possible solution.
Of course, it will take some time before clean energy sources replace fossil fuels, not only because fossil fuel reserves are at record high, but also because clean renewable energy sector has only started developing, and it needs certain period before being able to commercially compete with fossil fuels.