As the post above makes clear, carbon emissions and greenhouse gas emissions gathering in the atmosphere seem to be the principal cause of man-made climate change.
Many methods of generating power/electricity have the unfortunate side-effect of creating significant emissions that contribute to climate change. New types of energy, including nuclear energy, are seen as ways to reduce dependency on carbon-based (fossil fuel) energy.
To the best of our knowledge at this point, climate change is caused by something called the "greenhouse effect." The basic idea of this effect is that the sun's rays pass through the atmosphere and hit the Earth. Some of their energy bounces back off the Earth into the atmosphere. For the most part, when the energy reradiates from the Earth, it does so as heat, not as light. The heat goes back into the atmosphere and eventually radiates out of the atmosphere. However, carbon dioxide can trap that heat. Human activities, notably the burning of fossil fuels, add carbon dioxide to the atmosphere. That means more heat is trapped and climate change occurs.