OOPS stands for Out Of Phase Stereo. It is a simple technique used to process the two channels of modern stereo recordings into a "new", third channel, enabling us uncover "hidden" sounds in stereo recordings. The resulting OOPSed signal is a single channel, mono signal.
This process is also known as "Left Minus Right". When Quadraphonic recording was the rage in the seventies, OOPS or Left Minus Right was used as a cheap way of creating a new, third channel to increase the stereo listening experience.
The speakers (or headphones) of your stereo system convert an electrical signal into sound, by moving the speaker cone in relation to the postive and negative waves in the signal.
In the simple example of a pure tone, the electrical signal makes the speaker "oscillate" (move back and forth rapidly) by moving one way, outwards for example, on the positive (+) halves of the electrical waves, and move back the other way on the negative halves. The speaker cone movement makes the air in front of it move, and this frequently oscillating air reaches your ears as sound. This single wave is a "frequency" (how frequently the sound moves back and forth) and you hear it as a tone.
Recorded sound is made up of many of these elecrtrical waves in various combinations relating to the frequencies in the sounds being recorded.
Now, imagine two signals that are identical, except they are "out of phase" with each other, that is, that when one signal is having a postive wave peak, the other is having an identical negative peak.
If these signals are mixed together, they will cancel each other out. The positive peak of the first signal tries to make the speaker move out, but as it does, it is counteracted by the equal but opposite negative peak from the second signal, which tries to pull the speaker cone back in, so no sound results.
Now the good part!
In a stereo recording, some of the sounds are recorded on the left channel, and some are recorded on the right channel. However, because of the mixing done during the recording process, some sounds are on BOTH channels. It is very common in modern stereo recordings, for example, for the instruments to be in stereo (different) on both sides, and the vocal to be "in the middle", by having it mixed into both channels.
Now, if you took one of the channels of the above example and combined it OUT OF PHASE (plus to minus and minus to plus) with the other channel, whatever was THE SAME in both channels would cancel out, and you would hear only what was DIFFERENT in both channels. In our example, you would cancel the vocal, and hear only the instrumental accompaniment.