Atomic power, also called nuclear power, can come from two distinct types of reactions between atoms: fusion and fission. To understand these reactions, you must first know the basic structure of an atom. An atom consists of a positively charged nucleus in the center surrounded by negatively charged particles called electrons. The nucleus is made up of positively charged particles called protons and non-charged/neutral particles called neutrons. The number of protons and neutrons an atom has determines what kind of element it is, such as gold, iron, carbon, etc., and different elements combine to form different chemicals.
The electrons are attracted to the nucleus by a force known as the electrostatic force (i.e. negative charges attracted to positive charges).The protons and neutrons in the nucleus are held together by a much stronger force called the nuclear force, which happens only when particles are very close together (10-15 meters). Because the bond between the protons and neutrons is so strong, a lot of energy can be released when those bonds are broken.
Fusion occurs when nuclei from two atoms fuse to form one single atom. Fusion does not occur under standard conditions because the atoms must overcome the electrostatic repulsion that occurs when the two positively charged nuclei come together. When the atoms are forced together and come close enough to one another, the nuclear force overcomes the electrostatic repulsion and allows the two nuclei to become one.
In fission, one heavy atom splits to become two smaller atoms. Fission occurs because heavier atoms have greater electrostatic repulsion (i.e. more positively charged protons in close proximity to one another) than smaller particles. With enough positive charges, the electrostatic force overcomes the strong nuclear force and the large atom fragments.
In both cases, bonds between protons and neutrons are broken and more than a million times more energy is released than in average chemical reactions. Energy from fusion has been harnessed for thermonuclear weapons and fission has produced the atomic bomb. However, nuclear power can and is used peacefully within nuclear reactors to produce clean energy. Fission is currently used at nuclear power plants, but future power plants may use fusion instead.
If you would like to know more, there are some great resources online. One website that I like is this: atomic_power
Hope this helps