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Contact Stabilization adds artificial stiffness/damping to the contact pairs during the analysis, specially at the beginning to help keeping the parts from "flying away", and often there's no equilibrium until the contact is well stablished.
As it is artificial/numerical damping, this should be removed once the contacts are well defined.
that's why, usually, S1 =0.0, meaning the stabilization is fully removed, thus, ideally, the contact stabilization energy s zero at the end.
But for some more complex cases, it might be needed to keep some stabilization in order to converge the analysis.
This statement you've pointed gives you a general advice on trying to keep the stabilization energy as low as possible, to avoid adding too much energy into the system, that should not be there at the first place.
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