Where does gravity come from?

The most basic basic answer one could give is that gravity is caused by mass. This is essentially the answer that would have been given in Newton's era.

In 1916 Einstein published his Theory of General Relativity which quickly became (and still is) the best model for gravitation that we have. In Einstein's theory mass and energy are the same thing (consider his famous equation E = mc^2), therefore you might say that gravity is caused by energy (and all mass is energy).

Einstein's theory also offers a geometric picture of gravity; gravity consists of warps and curves in spacetime (caused by the presence of energy) which alter the paths of particles and give the 'illusion' of gravity.

The most in-depth answer currently available is that gravity is caused by the local Poincare invariance of the Laws of Nature. This basically means that you are free to use any coordinate system at any point in space and time and that the laws of nature are the same everywhere. This requirement automatically leads to Einstein's gravity. This is a result from quantum field theory. (Incidentally you can get the other forces of nature, such as the electromagnetic force from similar symmetry considerations).