The mass of an object warps space/time. This warping in the flow rate of time, and geometric warping of space, causes objects to want to accelerate towards the region of slower time flow. That is why an object will accelerate towards a massive body if it can fall towards it. We would fall towards the center of the earth if it weren't for the ground holding us back, but the accelerating force is always upon us, pinning our feet to the ground. As far as how mass warps space/time (the connecting mechanism) that is unknown.
Einstein believed that space was like a fabric , heavy objects warp the space around it, causing other objects to fall toward it. You can see this, stretch a fabric over an empty open topped container then put an apple or orange in the center, then put lighter objects like marble or walnut on the outside border of the fabric and it will roll toward the center, that's gravity
Space is like a fabric,once matter has enough mass it will begin to warp the fabric of space. When that mass gets around 300 miles in diameter, it is capable of creating it's own gravity. Dark matter keeps everything from flying apart.