Jefferson's intended meaning is the subject of some debate. Julian Boyd wrote an article on this in 1957, "The Smooth Handle: A Challenge to the Organization Man." Boyd believed that this statement embodied how Jefferson thought citizens of a republic should behave, and was descended from a similar saying by Epictetus, "Everything has two handles, one by which it can be borne; another by which it cannot." While debate was essential to a healthy republic, Boyd argued, Jefferson believed strongly that the exchange of ideas must always be civil, and he expressed this belief in his advice to "take things always by their smooth handle."
This is only one interpretation, however, and without an explicit explanation from Jefferson himself, each reader is free to interpret it as they will.