As I understand it, a system has a Fermi point when a single point in momentum space lies at the Fermi energy. In most systems there is either a Fermi surface (conductor) or no Fermi surface (insulator/semi-conductor). The existence of a Fermi point has interesting implications, though I don't know much about it. From the forward by Volovik in 'The Universe in a Helium Droplet':
"The system is either fully gapped, or the Fermi surface is developed, or, what has most remarkable consequences, a singular point in the momentum space evolves - the Fermi point. If a Fermi point appears, as happens in superfluid $^3$He-A, at low energies the system is governed by a quantum field theory describing left-handed and right-handed fermionic quasiparticles interacting with effective gauge and gravity fields. Practically all the ingredients of the Standard Model emerge, together with Lorentz invariance and other physical laws. This suggests that maybe our quantum vacuum belongs to the same universality class ..."