Phonons are produced by atomic vibrations and propagate through the media at the velocity of sound (At least acoustic one). They can also be produced by interaction of a material with particles or fields. For example, when an electron is moving in a medium, it might start the vibration of a atom causing creation of phonons and losing its energy. As like photon they behave as a particle with single spin, hence described by Bose Einstein statistics.
During their propagation, they interact with different particles and fields. Phonons which interact with the light are called optical phonons, which has higher frequency and hence energy than that of acoustical phonons which interact with sound waves. Acoustical phonons propagate along the material. Optical phonons frequency is measured through the coupling of their frequency with the frequency of rather week light (infrared) in a method called Infrared spectroscopy. Creation of optical phonons requires the vibration of two kinds of atoms against each other. While they vibrate against each other they will polarize their charge in certain direction. Once you have polarization of charge in a certain place, you will obtain electric field. This field can be coupled to the electric field present in light and in turn can be used to measure the frequency of phonons as in Raman Spectroscopy.
They play very important role in absorption of light and resistance of current.
Phenomena of superconductivity is described as phonon mediated process, in which two electron moves together unlike in metal where electron move alone, mediated by a phonon. Also the elasticity and plasticity of a material can be explained on the basis of phonons.
In summary phonon is a quantum mechanical unit of atomic vibration, which is related to the normal modes of vibration classical mechanics in which atoms of a medium move with the single frequency. Many physical phenomena can be described with the help of them in more fundamental way.