The increase in wavelength of rays and other energetic electromagnetic radiations that are elastically scattered by electrons is said to be the Compton effect.
It is a principal way in which radiant energy is absorbed in water.
Graphite is used in the Compton effect because:
The valence electrons are loosely bound into the atoms in the target material, graphite and it functions as a free electron.
Compton scattering is considered as important as it is the most probable association of high-energy rays in living beings with atomic nuclei.
It is used in radiotherapy.
It is also used in material physics to promote the wave function of electrons in matter.