For a given type of semiconductor material, such as silicon, the concentrations of holes and electrons are determined by the doping concentration.  Holes are electrons are constantly being generated, and they constantly recombine to achieve equilibrium.

Light shining on a semiconductor causes additional holes and electrons to be created, i.e. increases the generation rate.  The rate of carrier recombination increases when there are excess carriers, so eventually a new equilibrium is established, where the new recombination equals the new generation.  Removing the light, i.e. returning the generation rate to its original value, creates a temporary condition of excess carriers, and the recombination rate decreases to achieve the original (dark) equilibrium value.

Since the rate of recombination depends on the excess carrier concentration, the decay is an exponential decay process, and the time constant of this decay is defined as the carrier lifetime.

The excess carriers created by the light are dependent on the light intensity, and if the number of excess carriers produced is comparable to the majority carrier concentration, then there will be a noticeable change in the conductivity of the semiconductor material.  Thus, a plot of excess carriers versus time will be identical to a plot of conductivity versus time.