A Lyman-Werner photon is an ultraviolet (UV) photon in the one of the Lyman or Warner bands of molecular hydrogen (H2), which all reside in the 11.2-13.6 eV range. An H2 molecule 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. 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 whole range because the molecule vibrates (atoms oscillating toward each other and away from each other) at many small energy levels for each level of electron excitation and some of the 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 to dissociate. 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.