Stokes shift is the difference (in wavelength or frequency units) between positions of the band maxima of the absorption and emission spectra (fluorescence and Raman being two examples) of the same electronic transition. It is named after Irish physicist George G. Stokes.  
When a system (be it a molecule or atom) absorbs a photon, it gains energy and enters an excited state. One way for the system to relax is to emit a photon, thus losing its energy (another method would be the loss of heat energy). When the emitted photon has less energy than the absorbed photon, this energy difference is the Stokes shift. If the emitted photon has more energy, the energy difference is called an anti-Stokes shift; this extra energy comes from dissipation of thermal phonons in a crystal lattice, cooling the crystal in the process. Yttrium oxysulfide doped with gadolinium oxysulfide is a common industrial anti-Stokes pigment, absorbing in the near-infrared and emitting in the visible portion of the spectrum. Photon upconversion is another anti-Stokes process.
Stokes fluorescence 
Stokes fluorescence is the re-emission of longer wavelength photons (lower frequency or energy) by a molecule that has absorbed photons of shorter wavelengths (higher frequency or energy). Both absorption and radiation (emission) of energy are unique characteristics of a particular molecular structure. If a material has a direct bandgap in the range of visible light, the light shining on it is absorbed, causing electrons to become excited to a higher energy state. The electrons remain in the excited state for about 10−8 seconds. This number varies over several orders of magnitude depending on the sample, and is known as the fluorescence lifetime of the sample. After losing a small amount of energy in some way (hence the longer wavelength), the electron returns to the ground state and energy is emitted.
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