It's basically saying that the energy given off in the formation of four bonds is large enough to compensate for the energy required to promote the electrons.
What it means is that the needed amount of energy to promote the electrons is easily matched by the energy given off in the bonding stage. It might be easier to think of this like a normal reaction rather than promoting electrons. For example, the energy required to break the bond is the Cl2 bond is more than compensated by the energy released in the formation of the NaCl bond.
How, well we know that bond forming gives off energy, thus the energy required to promote the electrons is being matched, if not exceeded by the bonding.
Why, because if we have a reaction it's generally going to be a better and more stable reaction if it is exothermic. In this particular case, you need to give the atom the energy to promote the electrons, no energy, no promotion therefore no reaction therefore sad and bored Chemist.
Also, partly. It is saying that the electrons need energy to be promoted, + energy, but more energy is given out to keep the reaction working, lots of - energy, so we can say that energy from the reaction is allowing the reaction to work in a way.
Generally in the real world the reaction would take in energy from the world to promote the electrons, then repay this "debt" by the creation of bonds being exothermic.
Hope that helps