That helps explain curvature of space, but it doesn't explain any of the motion.
When you see those stretched rubber sheets, they rarely/never show the grid lines moving. So let's say you place a small *stationary* object at a specific grid point (coordinate), and there's a large object that deforms the grid itself. Nothing about that visual provides any new intuition about why the small object would leave it's current grid position and move towards the larger one.
The visual tries to explain gravity by appealing to your existing notion of gravity.
When you see those stretched rubber sheets, they rarely/never show the grid lines moving. So let's say you place a small *stationary* object at a specific grid point (coordinate), and there's a large object that deforms the grid itself. Nothing about that visual provides any new intuition about why the small object would leave it's current grid position and move towards the larger one.
The visual tries to explain gravity by appealing to your existing notion of gravity.