The Fermi velocity is the velocity that corresponds to the Fermi energy of a particle. The Fermi energy is the highest energy state of a particle in a system near absolute zero temperature.
Fermi energy only exists with respect to particles called fermions. Fermions are particles (such as electrons) that cannot share the exact same spin and energy level. In a metal, electrons are frequently able to move from atom to atom, which is why the material is conductive. However, the electrons still cannot share energy levels. Near the temperature absolute zero, the electrons are in the lowest energy levels possible. The Fermi energy corresponds to the energy that would be associated with the next highest energy rung in the system if one electron were to jump to that energy level. This corresponds to a kinetic energy, so the Fermi velocity is calculated using the kinetic energy equation: Ef = 1/2 x m x Vf.^2, where m is the mass of the electron, Ef is the Fermi energy and Vf is the Fermi velocity.