Conservation of Energy
Conservation of Energy is one of the most important principles to understanding how things work. The essence of this principle is that energy cannot be created or destroyed, but can only move from one object to another.
Energy is the ability to do work. That is, it is the ability of the object that has it to apply a force to another object. In the process of applying the force, the first object transfers energy to the second object. The longer the force is applied (or, to be more accurate, the greater the distance the second object moves while it is being applied), the more energy is transferred.
A pool ball sitting still on the table has no kinetic energy. A second pool ball coming at it with some velocity has a certain amount of kinetic energy. When the collide, the approaching ball transfers some of its kinetic energy to the stationary ball. After the collision, the first ball is in motion, and so has a certain kinetic energy. Because the second ball has transferred some of its kinetic energy to the first ball, it leaves the collision with less kinetic energy, and so with a smaller velocity. The total of the kinetic energies of the two balls after the collision must be equivalent to the total of their kinetic energies before the collision. In this case, that's the same as the kinetic energy of the approaching ball.
Atoms, or, to be more specific, the electrons in atoms have certain discrete energies they are allowed to have. The electrons can move from one energy level to another, but the difference in energy between the two levels must be compensated by some other energy change, somewhere else, in order to obey the principle of Conservation of Energy. If an electron moves from a higher energy to a lower energy level, the energy difference may show up in the creation of a photon with exactly that amount of energy. (Recall, the energy of a photon is proportional to its frequency, or inversely proportional to its wavelength.)
Conversely, an electron in a lower energy level may be moved to a higher energy level by the absorption of a photon.