HOW VOCAL REMOVAL WORKS
You can reduce the level of a vocal (or other lead instrument) in a stereo recording by taking advantage of how vocals are generally recorded: in mono and placed centered in the mix. Since the vocal track is present in both the left and right channels equally, you can, in theory, 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 affected. 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 thus 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 important drawback inherent in vocal removal is that, by definition, 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, and that will be described later.
Important note added November 21, 2002: You cannot remove vocals effectively if your source is an MP3 file. In order to remove vocals, the vocals in the left and right channels must be exactly identical. Then when the polarity is reversed in one channel and the channels are combined, anything common to both channels - what's panned in the center - is cancelled. But MP3 encoding processes the two channels separately, so they are not identical enough to cancel.
It is impossible to completely remove a vocal or reduce its level, without affecting other instruments in the mix. First, even though most vocals are placed equally in the left and right channels, stereo reverb is usually added to vocal tracks. So even if you could completely remove the raw vocal itself, some or all of the reverb is sure to remain, leaving an eerie "ghost" image. If you plan to record yourself singing over the resultant track, the new vocal can have its own reverb added, and you may be able to mix your voice loud enough to mask the ghost reverb from the original vocal track. Another limitation arises because vocals are not the only thing panned to the center of the mix. Usually, the bass and kick drum are also smack in the middle, and those get canceled along with the vocal! However, you can minimize this problem by rolling off the lowest bass frequencies on one channel before combining it with the other. Since one channel now has less low end than the other, the low frequency instruments will not completely cancel. In fact, of the software programs I've seen that offer a vocal removal feature, none alter the low end on one channel before combining, so the bass and kick are eliminated along with the vocal.
http://www.ethanwiner.com/novocals.html