This word can have two senses. It may refer to a restless tossing of the body in illness or to a boastful or false statement.
Of the two senses, you’re more likely to encounter the first, as it can still be found in medical writings; it can also refer to the nervous twitching of a limb or muscle. It comes from an older word jactation with the same meaning, which derives from the Latin jactare, to throw.
The other sense comes from the related Latin jactitare, to throw out publicly or to say in public. This became the English term jactitation for a public declaration or public or open discussion. In Tristram Shandy, Laurence Sterne referred to “much dispassionate enquiry and jactitation of the arguments on all sides”. The sense of boasting or bragging was often attached to the word, and the even rarer jactator means a boaster or braggart.
This sense is now pretty much dead in English, with its rare users employing it only for humorous effect. However, jactitation does still sometimes occur in legal contexts to refer to a false statement, picking up on the idea of boastfulness; in particular, it survives in the term jactitation of marriage, a false declaration that one is married to someone.