It is common to think that objects attract each other by their gravitational force. That is to say that most people have this idea that a massive body like the earth pulls on other massive bodies like the moon through some invisible force that we call gravity. When we imagine this, we imagine perhaps an invisible force field or beam that stretches from the earth to the moon, but this is not what is happening.
The earth does not pull on the moon and the moon does not pull on the earth. There is no force emanating from the earth or the moon. There is only space. And space touches everything. It pushes on everything. (This is what is called inertia?) And matter pulls back on space. In fact, matter comes from space. Matter is inertial mass energy that has condensed out of the vacuum energy of empty space.
But before we go there, lets go back to space pushing on matter and matter pulling on space. When enough matter gets together it pulls on space very hard and the more concentrated that matter is, the more focused is its pulling of space. This pulling of space bends space, and when space bends, it moves (accelerates) the matter that is floating within it.
We think of space as empty, but it is not. Space is a physical thing. It touches everything and everything touches it. Matter deforms space, stretching it, and this stretching is what makes other objects seem to travel in curved trajectories, but they don’t. They are traveling on straight lines across a curved surface.
A picture is worth a thousand words, so check out this video of differential geometry to see it.