jmw1137:
When normalizing, you scale the audio signal itself (=the wave file, in this case) up or down so the maximum volume level is, say, 90%.
Suppose you normalized a file peaking at 99% to 90% - it would have to be scaled down by 9%. All samples having a level of 9% or lower would be lost. By normalizing the file back to 99%, you couldn't reconstruct those samples, either.
When normalizing a compressed audio signal, there is another factor that influences the quality: The psymodel "intends" the encoded signal
only for the exact original volume. Any further modifications to the signal can, for example, pronounce artifacts or bring frequencies to the foreground that should actually be masked. (This problem applies to post-processing of compressed file in general, maybe not so much to normalizing, though - I don't know for sure. Anyway, it is a factor to consider.)
Somebody over at r3mix.net forums once gave a very nice and simple explanation of how MP3Gain works. You can look at the "structure" of an MP3 file like this (very simplified):
multiplier * (frame content)
The "frame content" is the audio signal itself, the volume of which the multiplier specifies. All MP3Gain does is to change the mutliplier value. It doesn't touch the signal itself, so any modifications made to the volume this way can be undone without any loss in quality.
BTW, the main reason why all these people tell you to normalize is that they think you can make files sound equally loud by doing so. That's not true.
Suppose you had a file A and a file B that you wanted to make equally loud. A shall be a song with the volume ranging around 60% most of the time, but peaking at 95%. B shall be a horrible modern compressed recording, ranging in the 90-100% area most of the time (peaking at 100%, of course).
As a novice who believes what most of those people say, you normalize both files to 98%.
A would be scaled up by 3% - a change hardly audible. B would be scaled down by 2% - also hardly audible.
The files would not even nearly have the "same volume", if B were played after A, you'd still grab your volume control immediately
MP3Gain modifies the volume of a group of files to make them sound equally loud (and it works!

).
Hope this helps,
Dominic
Edit: I just searched the r3mix forum for that explanation - according to the user who wrote it (VitaMan), is was deleted when the forum software crashed or something. (
...)