In the GR Einstein's interpretation was in terms of a deformation of the geometry of the space ending in a curvature of spacetime.
I've thought that mass could do this by interacting with other mass and causes gravitational waves which makes the space curved. But a prof told me that this isn't the case. For example the gravitational waves caused between the earth and the sun is just a very tiny effect which causes spiraling earth to the sun which is of little effect.
So mass is establishing the geometry of the space and the time. But the question remains how is mass doing that (curving spacetime)?