Yes, the dynamic nature of space-time and gravity as the manifestation of the curving effects of matter is the explanation of the "mechanism" as given by General Relativity. It works very very well; in other words the mathematical predictions have been experimentally confirmed.
However GR only deals with the macroscopic, and at the quantum level the theory does not apply. One of the fundamental issues is that the dynamic space-time, a premise of GR, is in contradiction to finite time, a premise of Quantum Mechanics.
The reconciliation of those two theories is a very current topic in the field of theoretical physics and is burdened with the difficulty of our current inability to perform extensive experiments that measure gravity using quantized matter such as a single particle.
Matt
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