Start with the classical representation. A compass points in the direction of North when taken out and laid down. What is happening is that the magnet in the compass is aligning with the external magnetic field of the planet Earth. That is the classical mechanic and there is a quantum analog, which is what this whole experiment deals with.
On the quantum level we express the magnetic moment using the Dirac equation for bodies that have no internal structure as µ = g(e/2m)S. The e is the elementary charge, the m is mass of the particle, and the S is the spin angular momentum of the particle. In quantum mechanics spin plays a major role in magnetic moments, so we must consider it here. That g is the g-factor that the experiment is dealing with. It is a dimensionless quantity that characterizes the magnetic moment and angular momentum. Basically it serves as the thing we tweak to ensure µ lines up with things we observe.
Take two electrons that strike each other. They have the same charge (negative) and thus, they should repel each other. But "HOW?", they aren't allowed to touch each so what pushed them away form each other? Like, really really does the pushing? Not that, oh well their charge fields touch each other. There's got to be "a something" that literally pushes them. And that is the exchange of a virtual particle. Getting into what a virtual particle is a deeper dive into the fields, but here's a quick run down.
The universe is a bunch of layers that we call fields all sandwiched together. So all the things that exist are just point in that field that are excited (that is they have energy to bring them to a level that we call existing). So an electron, that's actually just a point in the electron field that has enough energy that we call it actually existing. Now there could be a point in the field that has energy that's below that threshold of calling it actually existing. That's a virtual particle. Virtual particles participate in interactions, but can only do so if everything stays the same in the end and momentum is conserved. Like we can conjure a virtual electron and a positron (anti-electron) to exchange energy, but they must cancel each other out (by running into each an annihilating) in the end. There's way more, but that's outside what we need for this.
So picture two electrons hitting each other and then they bounce away. Something has to push them. That something is a virtual photon. As the electron on the left approaches the electron on the right, they fire off a virtual photon which reduces virtually the energy in the electron. However, this loss is virtual, the books must balance in the end. Which the photon on the right ALSO fires off a virtual photon, virtually reducing it's energy. The left electron absorbs the virtual photon from the right electron and vice versa for the right electron. Thus, the balance is maintained, the electrons return to their original energy. But! Momentum MUST be conserved. The photon from the left electron was moving right so now the right electron, having absorbed a photon moving right, must move rightward, the right electron was moving left towards the left electron, but now it is that motion MINUS the motion of the emitted virtual photon PLUS the motion of the right moving virtual photon. So this is what is actually pushing the electrons away form each other. This is what the repelling of two like charges actually is at a very deep level.
However, in the end the books just have to be balanced. So it's balanced in one virtual photon exchange, but there could be two virtual photon exchanges. As long as it's balanced, it's all the same. In fact, we could have five virtual photon exchanges. One of the virtual photons could summon up a virtual electron/positron that cancel each other out to make a virtual photon. There's no end to the number of exchanges that could happen, there's an infinite number of exchanges that could happen. Richard Feynman indicated that the more and more exchanges that could happen all impart smaller and smaller "corrections" to a calculated event. So basically, if there were 126,347,428 virtual exchanges between two electrons, the conserved values (that motion that we call repulsion) would change very, very, very, very, very, very little if there were 126,347,429 virtual exchanges. Basically after the tenth or so virtual exchange, the additional repelling that would be added by the eleventh virtual exchange would be insanely small, but not zero. And everything thereafter would just get smaller and smaller and smaller, but still measurable.