Elegant and delicate wit. Salt, both in Latin and Greek, was a common term for wit, or sparkling thought well expressed: thus Cicero says, “Scipio omnes sale superabat ” (Scipio surpassed all in wit). The Athenians were noted for their wit and elegant turns of thought, and hence Attic salt means wit as pointed and delicately expressed as by the Athenians. “Attic point,” wit.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894