This is a very intuitive explanation and I am trying to make it easy to understand rather then to match the math.
First, you have to learn that it is stress energy that bends spacetime.
Gravity itself has an effect of spacetime curvature.
Then you need to learn about the four speed vector.
The four speed vector is set up so that the magnitude has to be c.
Now you are asking about how it gives kinetic energy to an object. The object will move along a geodesic towards the center of mass.
If as you are asking the object is at rest relative to the earth, it is still moving in the time dimension.
Now as per GR, if the object is in the Earth's gravitational field, gravity will slow down the object in the time dimension. The object's vector component in the time dimension will decrease.
But the four speed vector's magnitude has to be c, so the spatial components of the vector will have to compensate, the spatial vectors will change. The object will start moving in space. It will move along a geodesic towards the center of mass.
Now you are asking what spacetime itself is. It is the mathematical model of 4D continuum, where time as the 4th dimension is just treated as another spatial dimension. Until the 20th century, they thought that time was independent of the spatial dimensions.