The Roman calendar did not have the days of the month numbered sequentially, instead it divided the month into three segments: Kalends, Nones and Ides. The Ides of March fell on the 15th of the month. For months with fewer than 31 days, the Ides fell on the 13th.
Julius Caesar was assassinated on the Ides of March in 44 BC. Caesar is said to have visited a seer that morning who told him that harm would come to him not later than the Ides of March. Caesar said, "Well the Ides of March has come," to which the seer replied, "They have come, but they have not gone."
The famous assassination is dramatized in Shakespeare's play, Julius Caesar, where Caesar is warned to "beware the Ides of March." Since the system of Kalends, Nones and Ides was in use well into the Renaissance, Shakespeare's audience would have been familiar with the term.