I'm not sure anyone really has a feel for it (although I'm sure someone does!), except to say it requires higher-dimensional thinking. They say it's a warping, or partial transposition of space and time.
I always figured if time's moving forward, then a little bit of that motion is being translated into space (hence if time were to reverse itself, so would gravity. My "proof" is in playing a video of something falling, backwards).
Of course the problem with that idea is that if time is "moving" forward, then it's moving as compared to what? When we say something moves through space, it's with respect to time, so what is time moving with respect to? I think the idea is that it's not... and neither does an object actually "move" through space. It's like individual still frames on a movie film. Motion is just the illusion created by the patterns & multi-dimensional geometric orientations of our physical reality.
When you notice that gravity is identical to a constant acceleration, also identical to a constant velocity around a circle (a warped path) - this is called centrifugal force. Inertia says that motion (and path) tends to remain constant, and there is a kind of resistance to any change. Since it is possible to replicate gravity with pure inertia of constant velocity in a curved path, it raises the question along with what is gravity... what is inertia? and why is inertia?
These are all different multi-dimensional (beyond 3 dimensions) viewpoints of the same one phenomenon. So what's the phenomenon?
The best way to understand it is to play with it in your imagination. That's what Einstein did!