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A Lyman-Werner photon is an ultraviolet (UV) photon in the one of the Lyman or Werner bands of molecular hydrogen (H2), which all reside in the 11.2-13.6 eV range. An H2 molecule in its ground state can absorb one, raising an electron's excitation. Subsequent emission of a photon has a chance of leading to the molecule's dissociation, i.e., splitting into atomic hydrogen. It is a case where a decrease in energy can lead to dissociation: a photon emission sometimes converts remaining "excess" energy into vibration between the two atoms of the molecule, which can be enough that the molecular bond no longer holds it together. UV within this range is called Lyman-Werner radiation (LW radiation) or Lyman-Werner flux (LW flux).
The molecule can absorb photon energies over this range (11.2-13.6 eV) because the molecule has many tiny energy levels of vibration for each energy level of electron excitation and some of the absorbed photon's energy can contribute to such vibration. Furthermore, the energy needed to dissociate the molecule is not constant, but depends upon the phase of the vibration's oscillation, and subsequent emission of a photon has a chance of leading to the criteria that produces dissociation. If the incoming photon had a higher energy, it could dissociate the molecule directly, but molecular clouds grow to be surrounded by HI regions that absorb ionizing radiation, and the two-step dissociation process is more common for the molecules screened in this manner. It is a means by which early stars counteract cooling of molecular clouds, suppressing star formation (star formation feedback).
This form of feedback has been of particular interest in the modeling the formation of Population III stars, given that metallicity was very low, giving clouds a lower cooling rate, making them less likely to reach the point of star formation.
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