It is the neon atoms that produce the primary laser light. The helium atoms provide collisions for energy transfer. The power supply transforms AC room current to DC needed to 'pump' the laser, that is, raise the energy levels of the atoms. The mirrors, carefully positioned turn the interior into a resonating cavity where the light can reflect back on itself and be amplified until it is ready to be emitted through the less reflective of the two. Inside the laser the electrical energy raises the atoms to excite states.
Most excited states decay very rapidly, others a little less so.
When an electron can stay in an excite state little longer, we call that state quasi-stable. When electrons move into quasi-stable states, it is possible to have many electrons in the medium in an excited state simultaneously. This is called population inversion, and is essential to the production of laser light. Once population inversion is achieved, electrons begin to drop back to lower energy levels, giving off photons of light in all directions. This is called spontaneous emission.