Probably more often than not, when people think of energy, one of the first things to come to mind will be fossil fuels. There are many other kinds of energy of course including kinetic, potential, nuclear and various other forms of chemical energy. Chemical energy includes fossil fuels but also includes all other forms of combustion including human and animal energy because metabolizing food is a slow, low temperature combustion process (essentially an oxidation reaction). In all chemical reactions, the energy extracted or put into the system comes strictly in the form of rearranging the outer electrons of the atoms involved in the reaction (through chemical bonding). When burning wood or fossil fuels, the energy given off comes at the expense of arranging the electrons in the reactants to be just a little bit closer to the nucleus of the atoms to which they are bound. In other words, the average bond strength is greater with the end products in combustion than was found in the initial ingredients.
If you are going to start off with just the bare electrons separate from an isolated nucleus, the positively charged nucleus and electrons would feel an attraction force trying to pull them together. The closer they come together, the stronger this attraction force becomes. The actual force law at play here is called inverse square because if you decrease the distance by three this electric force goes up by a factor of nine. Likewise if you decrease the distance by a factor of ten, the force goes up by a factor of 100.
So then if you start with a separated electron and a proton, the particles can do work by allowing them to come together. If you had enough of them pulling towards each other as they approach, you could in principle lift a weight, turn a crank or heat something and so extract energy from this approach to joining of the opposite charges.
Chemical reactions which give off energy allow the negatively charged electrons to on average come closer to each associated positively charged atomic nucleus through atomic bonding. By redistributing the outer electrons to allow tighter bonding on average between atoms, the electrons get closer to the positively charged nuclei and the difference between that from the starting and ending products is the amount of energy given off. In the same way that a lifted weight has potential energy to give off due to the gravitational attraction to the earth, loosely bound electrons have chemical potential energy. In the same way that a dropped weight can convert that potential energy into useful energy (such as turning a crank) redistributing more loosely bound electrons into more tightly bound electrons through chemical reactions can give off heat energy.
The majority of electrical energy in the world today comes from chemical combustion. Here fossil fuels are burned to create heat which in turn boils water which in turn creates high pressure steam which in turn expands into a turbine causing it to spin a generator which makes electricity. Nuclear energy can also be utilized to generate the needed heat to make electricity this way. The basic difference is the chemical reactor in a fossil fueled power plant is replaced by a nuclear reactor (and a very large litany of additional safety features).
The basic physics with nuclear energy are very similar to chemical energy in a certain sense. If you start with a disassembled nucleus of isolated protons and neutrons, they will experience the strong nuclear force when brought close together. They have to be brought close enough that the repulsion between identically charged protons is overcome by the strong nuclear force. It is this strong nuclear force that pulls all the protons and neutrons together in the nucleus of an atom. These particles are so closely bound together that the nucleus of an atom takes up only around one tenth of one percent of the volume of an atom yet contains over 99.9% of the mass. This strong nuclear force is so powerful that after breaking up the nucleus of large atoms like uranium in a nuclear reaction, the protons and neutrons in the end product atoms are able to assemble closer on average to each other than that from just a spherical nucleus cut in half. When any nucleus is split as done in nuclear fission, when the protons and neutrons in the split products reassemble into more tightly compacted configurations, they give off radiation typically consisting of gamma rays and electrons. The vast majority of the energy given off from this settling of any such nucleus in a reactor is generally realized as simple heat. Because the strong nuclear force is so powerful, the energy given off from such nuclear reactions is something around one hundred million times more energetic than that from a typical chemical reaction. In terms of being able to generate high temperature steam to turn a turbine and make electricity, nuclear energy has clearly found a niche creating baseload power to feed our energy hungry nation.