The answer you'll get to this question is that gravity occurs because space is curved. but it only looks curved in four dimensions, when you can look at the same space at more than one time. It's impossible to visualize as curvature in three dimensions.
It's similar to a light cone. It only looks like a cone in four dimensions. In our 3D space, it looks like an expanding sphere.
In three dimensions, space near mass appears compressed -- denser. It takes longer to pass through this space than it does ordinary space. Planet flyby paths are curved for the same reason light curves when it passes through a dense material: the geodesic path takes the least proper time.
Mass distorts the metric near it. Just by continuing to exist in time, mass broadcasts these compression waves out into space. They cause anything they pass through, like a star cluster, to move toward the source of the compression. It's like if you grabbed a tablecloth by the center, compressing the fabric, and pulled everything on the table slightly toward the middle of the table.