How does the precession of Mercury's orbit relate to relativity?

I understand that the changes in its orbit, and I understand that Newtonian mechanics could not explain this. What I can't seem to get is how relativity does explain its precession? What is the fundamental difference that relativity accounts for, and kinematics leaves out?|||As Mercury goes deeper in the Sun's gravitational well, the "local time rate" is slower, and the Sun's "frame dragging", pulls Mercury forward a bit more than Newton can describe.