relating to the part of the autonomic nervous system which balances the action of the sympathetic nerves. It consists of nerves arising from the brain and the lower end of the spinal cord and supplying the internal organs, blood vessels, and glands.
early 20th century: from para-1 'alongside' + sympathetic, because some of these nerves run alongside sympathetic nerves
parasympathetic in other Oxford dictionaries
Definition of parasympathetic in the US English dictionary