One theory of gravity is that it is caused by the curvature of space-time. An object with a large mass warps space-time more than one with a small mass. What we percieve as gravity is in fact the object moving along what, to it, in four dimensions, is a straight line.

Another theory is that the force of gravity is due to the excange of virtual gravitons, as electromagnetism is due to the exchange of virtual photons.