I believe they're referring to the idea of a gravitational force carrying particle, like photons for electromagnetism, W/Z bosons for the weak force, and gluons for the strong force. Typically this gets called a graviton but they've never been observed and the theories predicting them as far as I know don't predict that we can detect them in any meaningful/practical way right now which is also one of the problems for issues with a quantum theory of gravity.

I've always wondered (but not done the research/reading) on how that would mesh with black holes since you'd need gravitons to escape to mediate the curvature of space-time but that'd seemingly (to me) require them to be able to either ignore the curvature of space-time or travel faster than the speed of light in order to do so. And I believe that those two options there are actually mathematically equivalent as far as the consequences of things go.