Do we have theories about why gravity exists/how it works? For years I have been very fascinated by the "mystery" aspect of gravity. Functionally, we understand it for our applications, but in my (limited to my 3 quarters of undergrad general physics) understanding, we don't know why it exists or how the "pull" works. 
To provide an example of what I mean: there has to be some "measurable material" of gravity between, say, the earth and the moon -- some kind of 'graviton' (not that it needs to be a particle or anything, I have zero claims as to the nature of how gravity does what it does). The [butchered] saying of "pluck a flower and move the furthest moon" originates because gravity in theory, has an infinite range (right?) and moving a flower on earth could maybe move an atom on Jupiter ever so slightly.
Anyway, similar to how we had "very good" hypotheses about the existence of Higgs boson that the LHC 99%+ confirmed, do we have any "very good" hypotheses in regards to the fundamental way how gravity does what we have long-known it to do?
 A: Gravity may be fundamentally different from electromagnetism, as Wouter says, but it seems to me that, as far as your question is concerned, gravity is not fundamentally different from electromagnetism: there is gravitational field (http://en.wikipedia.org/wiki/Gravitational_field#General_relativity ), which is indeed "SOME "measurable material" of gravity between say the earth and the moon". AFAIK, you are right, and "gravity in theory, has an infinite range and moving a flower on earth could move an atom on jupiter ever so slightly." (I removed your "maybe" and question marks). However, in general, an atom on Jupiter does not "feel" a movement of a flower on Earth instantaneously - gravity is widely believed to have a finite propagation speed (http://en.wikipedia.org/wiki/Speed_of_gravity ) equal to the speed of light.
So again, it seems that, as far as your question is concerned, the situation with gravity is not fundamentally different from that with electromagnetic field: the Coulomb field has an infinite range, and there is "measurable material" - electromagnetic field (in the form of electrostatic field) between two charges, but, if one charge moves, the other charge does not "feel" that movement instantaneously. Thus, both gravitational and electrostatic forces are mediated by fields. One could say that gravitational field is just space curvature, but I don't feel that would change much. As for gravitons... Again, AFAIK, while it is not clear yet how gravitational field should be quantized (http://en.wikipedia.org/wiki/Quantum_gravity ), that does not seem to matter much as far as your question is concerned.  
A: Here is a theory about why gravity exists:
In a cosmological model that has a constant rate of expansion $\frac{\dot a}{a} = H$ and the expansion happens to all length scales, including the observer as in this link  Cosmology - an expansion of all length scales

Then gravity is explained as follows:
In the expansion of the type above each physical quantity $Q$ varies with time as $Q=Q_0 e^{nHt}$ where $n$ is the number of length dimensions.
Gravity is produced in nature to allow a scale-symmetric expansion of the universe without violating conservation of energy.
For an isolated mass its energy $mc^2$ becomes $(mc^2)e^{2Ht}$ and without gravity conservation of energy is violated.
However the total energy due to the mass in the universe of mass $M$ and radius $R$ is
$$\left(mc^2 - \frac{GMm}{R}\right)e^{2Ht} \tag 3$$
Energy can be conserved if
$$\left(mc^2 - \frac{GMm}{R}\right)e^{2Ht} = 0 \tag 4$$
and the strength of gravity is
$$ G=\frac{Rc^2}{M} \tag 5 $$
Small numerical constants omitted for simplicity.
The interpretation of this is that gravity is caused to allow the universe to have scaling symmetry.  The 'expansion' does not slow down or speed up as the universe expands. Energy is conserved during the 'expansion' due to the gain of internal energy of masses being of balanced by the gain of negative gravitational potential energy.
The flatness problem is naturally explained by (5).
Since no expansion is measurable in such a universe we have a stable, apparently static universe, always at critical density.
So this scaling symmetry is the reason behind the gravitational force and the reason that it's proportional to mass.
