with a waveform you have dynamics, peaks and valleys.
when normalizing(peak level) you are raising the loudest peak to whatever value you specify, normally 0. well, if the original waveform had a couple stray peaks that were allready near 0 but the rest of the wav was lower, then running the normalization(peak level) would only raise the enitre waveform until those stray peaks reached the desired level, thus appearing to do relatively nothing to the waveform in general.
if you run normalization(rms) on the same waveform it actually takes an average of the peak levels from across the waveform instead of using only the loudest peaks to adjust to 0(or whatever you desired). the problem with rms is that alters the dynamicsof the waveform, but this isnt allways a bad thing. that is why I said this is similar to runing a compressor , because it will take those stray loud peaks and bring them more inline with the rest of the waveform.
a compresoor gives you much more fine detail in controlling the resulting waveform than using normalization(rms) will