The true answer is that gravity still remains one of the biggest mysteries of physics.
Our modern view of gravity is based on Einstein's theory of general relativity. Einstein managed to show that the presence of gravitational field affects the motion of a body (which, in everyday life we refer to as "falling") in a completely identical way to that of the same body moving in straight line, but in a curved space (space-time, to be exact). Therefore, the effect of gravity can be thought of as curvature of space and time. According to this view, gravity is not a force at all (such as the electromagnetic force, etc.), but is a "curvature" of space-time. The origin of this curvature is of course the mass (or the energy, since E=mc2), of a given object, such as the earth. The object's mass causes the space-time to "bend" - therefore affecting the motion of other bodies, both massive and massless (photons) - which both "fall" towards it.
Thus, one can think of this question in terms of the origin of mass, or more precisely the energy of the universe, whose origin is really unknown.
One website with some more information (though, I am afraid, without much more insight) is