"Anger: an acid that can do more harm to the vessel in which it is stored than to anything on which it is poured"

The quote is recommending that anger, if not controlled or launched correctly, can be more harmful to the individual keeping it than to the individual or circumstance that caused it at first. The analogy used is that anger resembles an acid that can wear away the vessel (individual) in which it is held. Therefore, one must beware when holding onto anger for prolonged time periods.