Headphone Spatializaion is also known as ‘Binaural Sound’ or ‘Binaural Audio’. It is based on the idea, that when people hear direction, people do not only take into account the relative amplitudes of Left versus Right – aka panning – but that somehow, people also take into account time-delay that sound requires, to get to the more-distant ear, with respect to the closer ear. This time-delay is also known as the Inter-Aural Delay.
Quite frankly, if people are indeed able to do this, I would like to know how, because the actual cochlea cannot do this. The cochlea only perceives frequency-energies, and the brain is able in each hemisphere, to do a close comparison of those energies, between sound perceived by both ears.
If such an ability exists, it may be due to what happens in the middle ear. And this could be, because sound from one source, reaches each cochlea, over more than one pathway…
But what this also means is that if listeners simply put on headphones and listen to stereo, they too are relatively unable to make out positioning, unless that stereo is very accurate, which it is not, after it has been MP3-compressed.
So technology exists hypothetically, that will take explicit surround-sound, and encode it into stereo which is not meant to be re-compressed afterward, but that allows for stereo-perception.
There exist valid arguments against the widespread use of such technology. The way each person interprets the sound from his two ears, is an individual skill which he learns, in many cases people can only hear direction by moving their heads slightly, and the head of each person is slightly different anatomically. So there might not be any unified way to accomplish this.
What I find, is that when there are subtle differences in how this works over a large population, there is frequently a possible simplification, that does not correspond 100% to how one case interprets sound, but that works better in general, than what would happen if the effect is not applied at all.
Therefore, I would think of this as a “Surround Effect”, rather than as ‘Surround Sound’, the latter of which is meant to be heard over speakers, and where the ability of an individual to make out direction, falls back on the ability of the individual, also to make out the direction of his own speakers.