What is the meaning of the term excess in a general liability insurance policy?

An excess insurance policy is one, the coverage of which, sits "atop" the primary policy. That is, the excess policy provides additional indemnity benefits if or when the primary policy limits are exhausted.

In general, the primary insurer has a duty to settle a claim within its policy limits if it is possible to do so so as not to subject the excess policy to exposure. Normally, the excess insurer will track the underlying litigation to ensure that this is done. It may have a cause of action against the primary insurer if the primary insurer does not do this and the excess insurer is called upon to pay the claimant.