Is quantum physics actually an improvement in the theory of how reality works?

It explains everything microscopic. For example, the stability of atoms. Why doesn't an electron just spiral into the nucleus and stay there? The uncertainty principle means it can't be both localized at a point and have a fixed momentum of zero. If the position wavefunction is a big spike concentrated at a point, then the momentum wavefunction, which is the Fourier transform of the position wavefunction, will have a nonzero probability over a considerable range of momenta, so the position wavefunction will start leaking out of the nucleus in the next moment. The lowest energy stable state for the electron is one which is centered on the nucleus, but has a small spread in position space and a small spread in momentum "space".

However, every quantum theory ever used has a classical conceptual beginning. You posit the existence of fields or particles interacting in some classical way, and then you "quantize" this. For example, the interaction between electron and nucleus is just electromagnetism, as in Faraday, Maxwell, and Einstein. But you describe the electron (and the nucleus too, if necessary) by a probabilistic wavefunction rather than a single point in space, and you also do the same for the electromagnetic field. Curiously, when you do this for the field, you get particles as emergent phenomena. A "photon" is actually something like a bookkeeping device for the probabilistic movement of energy within the quantized electromagnetic field. You can also get electrons and nucleons (and their antiparticles) from fields in this way, so everywhere in elementary particle physics, you have this "field/particle duality". For every type of elementary particle, there is a fundamental field, and vice versa. The basic equations that get quantized are field equations, but the result of quantization gives you particle behavior.

Everyone wants to know how to think about the uncertainty in quantum physics. Is it secretly deterministic and we just need a better theory, or do things really happen without a cause; does the electron always have a definite position even when we can't see it, or is it somehow not anywhere in particular; and so on. These conceptual problems exist because we have no derivation of quantum wavefunctions from anything more fundamental. This is unlike, say, the distributions in ordinary probability theory. You can describe the output of a quincunx using the binomial distribution, but you also have a "microscopic model" of where that distribution comes from (balls bouncing left and right as they fall down). We don't have any such model for quantum probabilities, and it would be difficult to produce (see: "Bell's theorem"). Sum over histories looks like such a model, but the problem is that histories can cancel ("interfere destructively"). It is as if, in the quincunx device, there were slots at the bottom where balls never fell, and you explained this by saying that the two ways to get there cancelled each other out - which is how sum-over-histories explains the double-slit experiment: no photons arrive in the dark regions because the "probability amplitude" for getting there via one slit cancels the amplitude for getting there from the other slit.

As a practical matter, most particle physicists think of reality in quasi-classical terms - in terms of fields or particles, whichever seems appropriate, but then blurred out by the uncertainty principle. Sum over histories is an extension of the uncertainty principle to movement and interaction, so it's a whole process in time which is uncertain, rather than just a position.

The actual nature of the uncertainty is a philosophical or even ideological matter. The traditional view effectively treats reality as classical but blurry. There is a deterministic alternative theory (Bohmian mechanics) but it is obscure and rather contrived. The popular view on this site is "the many-worlds interpretation" - all the positions, all the histories are equally real, but they live in parallel universes. I believe this view is, like Bohmian mechanics, a misguided philosophical whimsy rather than the future of physics. Like Bohmian mechanics, it can be given a mathematical and not just a verbal form, but it's an artificial addition to the real physics. It's not contributing to progress in physics. Its biggest claim to practical significance is that it helped to inspire quantum computation; but one is not obliged to think that a quantum computer is actually in all states at once, rather than just possibly in one of them.

So, I hold to the traditional view of the meaning of quantum theory - that it's an introduction of a little uncertainty into a basically classical world. It doesn't make sense as an ultimate description of things; but I certainly don't believe the ideas, like Bohm (nonlocal determinism) or Everett (many worlds), which try to make a finished objective theory by just adding an extra mathematical and metaphysical facade. The extra details they posit have a brittle artificiality about them. They do link up with genuine aspects of the quantum mathematical formalism, and so they may indirectly contribute to progress just a little, but I think the future lies more with the traditional view.