Since Mass and Energy are different manifestation of the same thing, yet Mass and Gravity are inter-related, I guess the better question would be "What is Mass?" Given that Mass, however small, is bound by speed of light and does contribute to Gravity while its altered-ego (Energy) does not (travels at c and causes no Gravity, although it does follow Geodesic path), what is it about Mass that shows these properties?
Also, just for fun, is this possible? If one were to be able to convert Energy to Mass and back at will, wouldn't a Gravity-Drive be possible by repeatedly creating Mass (and converting back to Energy) in front of a spaceship? Of course, we are talking about huge amount of Energy and efficiency is always a concern, but I suppose it is possible.