Usually atoms have the tendency to return to ground state releasing the absorbed energy. Hence, the population of atoms in ground state is greater than that of excited state. For laser action, there should be more number of atoms in higher energy state.
Artificially creating more number of atoms in a higher energy states than the lower energy state is called population inversion. The chances of stimulated emission taking place increases when the state of population inversion is achieved in the medium.
The ratio of population of atoms in the energy states is fixed by the Boltzmann equation $N2/N1 = e(-(E2-E1)/KT)$
The negative exponent indicates that N2< N1. But for stimulated emission to dominate N2 should be made greater than N1. This is possible if T is negative. Therefore, population inversion is known as state of negative temperature. Here negative temperature does not means lowering of temperature below zero degree.
It only means maintaining a non-equilibrium state.