An LDR is a piece of semiconductor designed to be exposed to external illumination. At very low temperatures, a semiconductor is basically an insulator because it does not have any mobile charge carriers to carry a current. The illumination provides the energy to “loosen” some electrons from the atoms. These electrons are mobile and capable of carrying a current. So the more brightly the LDR is illuminated, the higher the charge carrier concentrations (more charge carriers per unit volume). This lowers the resistivity of the semiconductor and thus the resistance of the LDR.
As the I-V graph reveals, a LDR has a different constant resistance at different intensity L of the illumination. The more light it receives, the lower the resistance.