There are two explanations.
The first is Einstein's General theory of Relativity. In this matter causes space to curve and this curvature of space time causes the attraction.
This explains why massive bodies like the sun can cause mass-less light to bend around it. it also explains the deviation in Mercury's orbit and other phenomina which cannot otherwise be explained.
There is also a theory derived from the other force laws that explain Electromagnetic and the nuclear forces. In this a mass-less virtual particle called the graviton transmits the force between two bodies.
There is no evidence for this second theory yet - no one has found the graviton. The belief in it is because people think that gravity "should" work like all the other forces.



