The goal in laser operation is for the excited helium atom to collide with a de-excited neon atom and to boost/excite the latter into a higher-energy metastable state. If the two energies were not a close match, this selective transfer of excitation energy wouldn’t happen.
Work Step by Step
This is shown in the textbook's energy level diagram. Because of the fortuitous match in energies, collisions between excited helium metastable atoms and ground state neon atoms results in an efficient transfer of excitation energy from the former to the latter. These collisions excite the neon atoms into the desired metastable state, creating a population inversion in the neon atoms.