Most programs that "normalize" sound files do so by adjusting all the samples so that the loudest single sample is at some specified value. This is not a good way to make all the files actually have the same loudness. First of all, the human ear does not hear the loudness of single samples. It averages out sounds over time. Secondly, today's popular music CDs are heavily compressed. The sound engineers making the CD raise the average level so that it sounds much louder, while compressing the loudest parts so that they don't distort. A typical uncompressed sound file might look like this:
A typical compressed sound file might look like this:
Both of these files have a peak sample at about 100%, but the compressed file has a much louder average level. It sounds much louder when played back. So to do actual loudness normalization instead of peak normalization, we need to calculate how loud the file actually sounds. MP3Gain uses the Replay Gain algorithm to calculate this loudness.
The bad news: MP3Gain can only adjust the volume of your mp3 files in steps of 1.5 dB.
The good news: 1.5 dB is a small enough step for most practical purposes. Most humans can just barely hear a volume change of 1 dB.
The other good news is that this volume adjustment is completely lossless. In other words, if you adjust an mp3 by -6 dB and then change your mind, you can adjust it again by +6 dB and it will be exactly the same as it was before you made the first adjustment.
Here's the technical reason why it's lossless, and also why the smallest change possible is 1.5 dB:
The mp3 format stores the sound information in small chunks called "frames". Each frame represents a fraction of a second of sound. In each frame there is a "global gain" field. This field is an 8-bit integer (so its value can be a whole number from 0 to 255).
When an mp3 player decodes the sound in the frame, it uses the global gain field to multiply the decoded sound samples by 2(gain / 4).
So if you add 1 to this gain field in all the frames in the mp3, you effectively multiply the amplitude of the whole file by 2(1/4) = 119% = +1.5 dB.
Likewise, if you subtract 1 from the global gain, you multiply the amplitude by 2(-1/4) = 84% = -1.5 dB.