The mechanism of air ionization by a single nanosecond discharge under atmospheric conditions is studied using numerical simulations. The plasma kinetics are solved with ZDPlasKin and the electron energy distribution function is calculated with BOLSIG+. The model includes the excited electronic states of O and N atoms, which are shown to play the main role in plasma ionization for ne > 10 16 cm-3. For electric fields typical in nanosecond discharges, a non-equilibrium plasma (Te > Tgas) is formed at ambient conditions and remains partially ionized for about 12 nanoseconds (ne < 10 16 cm-3). Then, the discharge abruptly reaches full ionization (ne ≈ 10 19 cm-3) and thermalization (Te = Tgas ≈ 3 eV) in less than half a nanosecond, as also encountered in experimental studies. This fast ionization process is explained by the electron impact ionization of atomic excited states whereas the fast thermalization is induced by the elastic electron-ion collisions.