Nearly all of the energy that we use is nuclear.

Most of our power comes from the sun, which is running nuclear fusion in its core (it's basically a giant hydrogen bomb that is so massive that its gravity keeps it from blowing apart). This is the energy that makes plants grow, and thus is the energy that keeps anything that eats plants (or anything that eats anything that eats plants) alive. Even fossil fuels were made originally from solar energy in the distant past by tiny algae in the ocean.

The other source of energy we use comes from the breakup of heavy radioactive elements like uranium. This is the source of energy that keeps the interior of the Earth hot. When we use geothermal energy, this radioactive decay is where that heat is ultimately coming from. It's also what we use in a nuclear power plant, since we haven't yet mastered nuclear fusion except in bombs.

The only source of energy that we use that is not nuclear is the tides, which is gravitational rather than nuclear. The moon as it orbits the Earth exerts tidal forces on the Earth's crust and oceans, and using turbines we can harness this energy, ever-so-slightly slowing down the Earth's rotation as we do so (although it will take hundreds of millions of years for this to stop!).

Nuclear energy, or energy produced from nuclear reactions, is the same as energy produced by any other generation method. For example, nuclear reactions in a nuclear power plant generate large amounts of heat, which is usually used to drive steam turbines, which creates electrical power. A coal power plant operates on the same principle: the coal is burned, which drives steam turbines to create electrical power. Energy produced by nuclear reactions, burning coal, solar panels, windmills, or any other method is exactly the same when it reaches your house through the power lines.

So, people use nuclear energy when nuclear reactions are chosen by the community as the way to generate energy. Choosing which method to generate energy is not easy, however, since each method has advantages and disadvantages. And, research on new methods of energy generation is occurring every day. In the future, most energy may come from a single energy generation method, but for now energy will come from many places, including nuclear reactors.