Means "advice, counsel" or "council, assembly" in Italian, a nickname for a wise, thoughtful, or perhaps fearful individual, or an occupational name for a member of a council.
Derived from the medieval given name Consilius, or from a short form of the auspicious name Buonconsiglio "good advice", associated with the Marian title Madonna del Buon Consiglio "Our Lady of Good Counsel".