Q: "How do vocal removers really work?"

A: Vocal removal takes advantage of the way vocal tracks are normally mixed in a stereo recording: centered, with an equal and identical signal coming from the left and right speakers. You can remove it (or at least reduce its level) by subtracting one channel from the other. Instruments panned away from center will not be removed, although the tone of those instruments will probably be effected. The basic procedure is to reverse the polarity of one channel, and then combine that with the other channel. Any content that is common to both channels will be canceled, leaving only those parts of the stereo mix that are different in the two channels. Reversing the polarity of an audio signal means that the parts of the waveform having a positive voltage are made negative, and vice versa. (This is often incorrectly called reversing the phase.) One drawback of vocal removal is that it reduces a stereo mix to mono. Since you are combining the two channels to cancel the vocal, you end up with only one channel. However, there are ways to synthesize a stereo effect afterward. Some devices apply additional signal processing and equalization, but pretty much all begin the same way.