String theory is a field of theoretical physics which suggests that the smallest form of matter, smaller than atoms, neutrinos or quarks, are tiny circular strings. These strings vibrate, affecting adjacent strings, with the frequency of their vibration determining their physicality (density of matter, for instance).
Singularity is set in a far-future universe in which mankind has harnessed manipulation of strings. String resonance refers to the deliberate manipulation of string vibration in order to affect matter. This can have almost limitless effects, from the suppression of player character abilities or ailments, to levitating platforms and touchable holography.
In other words, string resonance is Singularity's version of "a wizard did it." Although it's a legitimate branch of theoretical physics, just know that how we're using it in the game boils down to "whatever we need." When in doubt, strings did it.