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.