Feeling is, above all, knowing, having a picture in your head of where the ball's gonna go if you hit it in any particular way. It's about making it all look calculated without actually calculating any of it, the shot comes instinctively.
We're all used to hitting balls that have a certain speed and rotation and those are the ones you encounter 90% of the time in rallies. If you're good at table tennis, they're easy, they're bread and butter and people won't refer to someone hitting those sort of shots as someone with great feeling. When, however, an awkward ball comes - the ability to put it anywhere on the table, as if by hand, is the Feeling. That's why you usually hear it from the commentators when there's a net ball, side spin, a touch or drop shot, these kinda things involved.
Practice is paramount, when you've seen them all and hit them all, the more the better, your brain will just do the maths on its own without your interruption.