If you are talking about "nuclear" atomic energy, then there are two main sorts.
Fission energy: This is where the natural tendency for some radioactive elements (usually isotopes of Uranium, although other metals have been used, notably recently, thorium) to decay, releasing energy whilst doing so. In controlled conditions the product of decay (a free neutron) is used to cause a "chain reaction" by impacting upon (bad use of words, probably) another unstable atom, which itself decays and releases more neutrons. This entire self-sustaining process generates heat which is usually used to boil water for steam turbines.
Fusion energy: This is where two nuclei (usually of hydrogen) are forced together at extremely high pressure and they fuse together to make a new element. In doing so, mass loss is converted to energy. This is the power behind the sun, where hydrogen fuses to helium, and in thermonuclear weapons (H-bombs). It has yet to be harnessed for peaceful energy generation (but people are still trying).
