Heat of reaction for the decomposition of AgCl means?
The intent of the question is that the reaction:
$$ \ce{Ag+} + \ce{Cl-} \rightarrow \ce{Ag} + \ce{Cl}$$
requires absorbing exactly one photon. That photon must have at least the energy required to perform this reaction. The grey colour produced is caused by the metallic silver ($\ce{Ag^0}$) formed by the reaction.
Because a photon's energy is inversely proportional to its wavelength, $E_{photon}=\frac{h c}{\lambda}$, in order to have the required energy or more to cause the reaction, the photon must have a required wavelength or less.  So there is a maximum wavelength that the photon may have in order to cause this reaction.
You're told that the energy required to decompose 1 mole of $\ce{AgCl}$ is 248 kJ/mol, so you have to figure out the energy per atom/photon and convert that energy to a wavelength.
This is an example of the photoelectric effect - that light comes in quantised particles (set amounts of energy) called photons, and certain processes require absorbing a single photon at a time with enough energy, rather than absorbing more lower energy light over time, as if the light was only a continuous wave.