The previous answer described gravity in the Newtonian sense, but Einstein had a very different explanation. He said that massive objects cause space to warp (like placing a bowling ball on a trampoline). Massive objects are "attracted" to other massive objects because they fall into these gravity wells. Thus, there is no energy conversion, only a tendancy for objects to follow the path of least resistance through space (as when you place a marble on the edge of the trampoline and it "falls" inward toward the bowling ball).
How much mass is Earth converting to energy per unit time to generate its gravity?