If you really want it:
Electrons, as a fundamental particle, behaves like a little magnet. This magnet can have two orientations in an applied magnetic field: with the field, or against it. The energy of the two directions are slightly different (poor analogy of going with or against the flow).
Note without an applied field there is no effect, but when you place the H atom in the said magnetic environment, you will obtain two possible energies in one orbital. Hence a splitting.
There is more explanation as to why there's only two, but not 4. Part of that's to do with sub shells of atoms, the basic s shell is completely symmetric and an electron in that shell has no magnetic interactions whatsoever.