My naive understanding of GR is that gravity is curvature of spacetime caused by massive presence which causes that curvature around it. So mass affects surrounding spacetime and the curvature effect is gravity which affects other masses within effective reach of that curvature called gravity which causes gravitational interaction between masses towards each other. Then gravity is the curvature but the curvature is caused by masses, so masses make gravity by curving spacetime.
Spacetime, or the curvature of spacetime, is not itself the cause of gravity, it is the result of gravity— it is a description of what the interaction of objects, in space over time, looks like to us! — Decribed in four dimensions.
Gravity does require the presence and interaction of mass, with either another mass or some form of energy, such as light— as in photons.
General Relativity is a description of how things interact, not what causes the interaction. IE GR does not describe what causes gravity— that is at least at present, something being approached from the context of quantum mechanics, in a variety of ways... So far without significant success.
In a very crude way you could think of the curvature of spacetime as like a whirlpool in a river, which is caused by the dynamics of how the water in the river and the riverbed interact... In the case of gravitation, we know that mass must be involved (the riverbed), but the nature and "substance" of spacetime (the water), in practice remains unclear... And thus the mechanism of gravitation, also remains unclear...
Personnally, I believe there is some promiss in approaching the underlying mechanism from the perspective of "Induced Inertia" and it seems to some lesser degree, from what I understand of "Induced Gravitation". (See papers by Puthoff, Rueda, Haisch & others, for information on "Induced Inertia and Gravitation.)
