I think to the contrary that the Stern-Gerlach experiment is one of the best understood examples for quantum dynamical behavior and the basic features of quantum theory, including the theory of measurement. So, what do you mean by "nobody gets it"?
Spin can be understood from various points of view. First of all there is the phenomenological point of view: Spin is a feature of some elementary particles associated with a magnetic moment and thus it can be investigated by the movement of these particles in a magnetic field, and that's how it was discovered by Stern and Gerlach. Their ideas about the phenomenon were of course very incomplete and within the then known way to describe quantum phenomena, namely in terms of the Bohr-Sommerfeld model, which already then was known to be incomplete at best, if not inconsistent in itself. As we know today, with the discovery of modern quantum theory in 1925, the latter is indeed the case.
Form the point of view of modern quantum theory, spin is very well understood. The most convincing way to derive and understand it, is to use group theory. Group theory and group representations on the Hilbert space as used in quantum theory are anyway a very important ingredient of modern physics. The idea is to use very basic facts about the mathematical structure of space-time, here the Galilei-Newton space-time model. The space-time can be described by its symmetries (translation invariance in time and space, isotropy of Euclidean space, invariance under Galilei boosts), and in order that the quantum theory of a system like a particle is consistent with this space-time structure, it should admit the representation of the corresponding Galilei group of symmetry transformations of space-time. An "elementary particle" is then defined as being described by an irreducible ray representation of this group, which can be induced from a unitary representation of an appropriate central extension of its covering group. This is quite technical, but the upshot of this mathematical analysis is that an elementary particle is charcterized by its mass (which is also known from macroscopic "point like" objects) and its spin (which is not really known from classical mechanics; the most close analogue is an extended body that may rotate around its center-of-mass point, which itself is at rest; that's where the name spin for this angular-momentum quantum mechanical observable comes from).
Then you can ask, how electromagnetic fields act on such particles. There you have the additional principle of gauge invariance and the most simple realizations to build the corresponding Hamiltonian is, what's called minimal coupling, meaning that you couple the electromagnetic potentials to the electric charge and current provided by the particle. In non-relativistic theory this procedure is unfortunately not a unique, but one of the realizations of minimal coupling leads for spin 1/2 (the most simple case of a particle with spin) to the Pauli equation, which itself can be derived also as the non-relativistic limit of the relativistic Dirac equation for a spin-1/2 particle in an electromagnetic field, and for the relativistic QFTs the principle of minimal coupling is a pretty unique procedure. So there is some logic behind the spin and the implications of its existence to particle dynamics in the electromagnetic field.
The Pauli equation then admits in a not too complicated way to investigate the deflection of a spin-1/2 particle in a inhomogeneous magnetic field, which leads to an accurate description of the Stern-Gerlach experiment. It's particularly intuitive since the semiclassical description turns out to be a very good approximation in the typical setup of the classical experiment.
