When we see something in the distance, or out of the corner of the eye, or in fading light–the mind will offer an identity or name for what we think we see, but one that proves false on drawing nearer: it’s that intersection that I’m after–the instant between where you think you know what you are seeing, when the imagined image is replaced by an object with a name, with a received place in external reality.  In a work of art, that would be the power to suggest, to raise the question–but to resist capture by withholding the answer–that the viewer remain at an intersection between what is out there , and the hidden desire that is source of the art’s affective power.
In refusing to ‘represent,’ (to point to something else, something ‘out there,’ the work becomes a mirror reflecting back on ourselves, on a struggle we have not been aware of, until, agitated by being unable to find what the art is pointing to–a disturbance that may help open us to what we have been struggling NOT to see.
I think that happens with any work of art; even most explicitly representational work is always a distortion–and it’s in the distortion that we can see ourselves. Those brought up with, and open to experiencing art, will find this in any style or genre.
Non-representational art merely places this at the center, by erasing the distractions.