PL intensity is the absolute value you obtain from the measurement.
As for normalized PL intensity, it depends "to what" it is normalized.
In general, normalization is used for a better qualitative comparison of two or more spectra. For instance, when measuring samples of different thickness, you may want to exclude the contribution of thickness from the analysis of the results: to do so, you can normalize PL intensity "to the thickness" by simply dividing the absolute PL intensity of each sample by its thickness. In this way, normalized PL spectra (unlike absolute PL spectra) are not dependent by the thickness.
The PL intensity is simply the maximum peak intensity that you can measure on your as is spectrum. However a way to normalize the PL intensity is to divide the whole spectra by the relative intensity or by the intensity of a selected peak when you have several peaks. In the later case we call a normalization with respect to a given peak.
Generally the intensity of the peak is not very significant, it's better to use the integrated intensity .
When you obtain PL intensity from the experiment, you have a relative peak photo-induced by the laser with arbitrary units.
If you normalize your spectra, you are just adjusting the maximum peak at the unity. The normalized option is very usefull when you want to compare energy peak positions between different experiments.
It is very difficult to quantify the PL emission (e.g. determine the actual photon flux) in an actual experiment and consequently it typically makes more sense to show the normalised PL intensity. Typically one can extract already a lot of information from the wavelength dependent relative PL intensity without knowing the actual photon flux (see e.g. Wurfel, P., Trupke, T., Puzzer, T., Schaffer, E., Warta, W., & Glunz, S. W. (2007). Diffusion lengths of silicon solar cells from luminescence images. Journal of Applied Physics, 101(12), 123110. doi:123110 10.1063/1.2749201 for a nice application for silicon wafer solar cells).