Potential energy refers to stored energy - a bowling ball in the top of a closet has gravitational potential energy - if you allow it to fall, it will do some work (perhaps on your toes!) by virtue of the gravitational force between the earth and the ball. Nuclear energy refers to the potential energy stored inside atomic nuclei, by virtue of the strong nuclear force between protons and neutrons (as well as the stored electromagnetic energy between the protons). This picture is of the "Dakota" H-bomb test almost 50 years ago over the Pacific. An H-bomb fuses isotopes of hydrogen to form Helium, releasing stored nuclear energy . This particular explosion released energy (ultimately in the form of electromagnetic radiation, sound, heat, shock wave, etc) equivalent to exploding a Million tons of TNT (1.1 MTon). This is a lot of energy - very roughly like filling our football statium up to the brim with TNT. In metric units, that's about 4E15 Joules, comparable to the amount of electrical energy produced in a typical power plant over a year. By comparison, the explosion over Hiroshima, which was an "A-bomb" (fission of Uranium), produced about 12 kilotons of energy (about 100 times less)

More generally, the question of where we will get energy to supply our technological society during our lifetimes, (and what the corresponding environmental costs and issues are) is one of the must pressing and fascinating scientific questions I can think of. The topic is huge - here are some links from a course on Energy and the Environment I taught a couple of years ago, if you're interested.