Nuclear power is important for at least two main reasons.
First, nuclear power is important because it is a form of electric power that does not contribute to global warming. Our modern world consumes huge amounts of electricity. All of the cell phones and computer devices that we use require a great deal of power. Much of this power is generated by burning fossil fuels. This burning emits greenhouse gases and adds to the problem of global warming. Therefore, it is very important to find ways of creating electricity that do not burn fossil fuels. Nuclear power is one such way. The process of making electricity via nuclear power does not emit any greenhouse gases.
Second, nuclear power is important because it presents us with a major dilemma. While it does not produce greenhouse gases, it does have the potential to accidentally emit radiation. Such accidents, like the one in Japan in 2011, can devastate large areas of land, making them unfit for human habitation. What this means is that we have to decide between the possibility of terrible nuclear accidents and the certainty of global warming caused by fossil fuel usage.