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Mass tells space how to curve. Curved space tells matter how to move. What you call gravity is geometry — the shortest path through a bent universe.
The left side describes the geometry of spacetime — how it curves and twists. The right side describes the matter and energy that bends it.
An orbiting planet is not pulled by an invisible force. It is following the straightest possible line — a geodesic — through a universe whose shape has been altered by mass.
The rubber-sheet metaphor is imperfect (it uses gravity to explain gravity), but the underlying mathematics describes black holes, gravitational waves, the bending of starlight, and the expansion of the universe — all confirmed by experiment.