The term hyperfine structure refers to a collection of different effects leading to small shifts and splittings in the energy levels of atoms, molecules and ions. The name is a reference to the fine structure which results from the interaction between the magnetic moments associated with electron spin and the electrons' orbital angular momentum. Hyperfine structure, with energy shifts typically orders of magnitude smaller than the fine structure, results from the interactions of the nucleus (or nuclei, in molecules) with internally generated electric and magnetic fields.
In atoms, hyperfine structure occurs due to the energy of the nuclear magnetic dipole moment in the magnetic field generated by the electrons, and the energy of the nuclear electric quadrupole moment in the electric field gradient due to the distribution of charge within the atom. Molecular hyperfine structure is generally dominated by these two effects, but also includes the energy associated with the interaction between the magnetic moments associated with different magnetic nuclei in a molecule, as well as between the nuclear magnetic moments and the magnetic field generated by the rotation of the molecule.
Read more about Hyperfine Structure: History, Theory, Measurements
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