For a molecule to fluorosce it has to relax the lowest- energy state from the excited state with emission of photon- which is called fluorescene. The difference in this energy( excited state- ground state) is called the Stokes shift.
However, there are other mechanisms available for molecule in the excited state to relax back to the ground state. Phosphorescence and luminescence are two other mechanisms of relaxation that involve such emission of photon. There are mechanisms which do not involve emission of photon for relaxation - like relaxation back to the ground state in internal conversion, where energy is conserved by the molecule by dissipating heat to the surrounding.
Another explanation to this is molecular rigidity. If the molecule looses the energy incident on it in rotational and vibrational motions , then its not going to fluoresce. Only highly rigid oleculs are fluorescent.
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