Before we get to the "beware" part, lets start with the basics. The Ideas of March, or Idus Martiae in Latin, is the day in the Roman calendar that corresponds with March 15.
According to an article on History.com, the term originally comes from the way that dates were calculated to create the calendar: "At the time, dates were expressed in relations to the lunar phase of the month using three markers: Kalends (Kal), Nones (Non) and Ides (Id). The first phase of the moon, the new moon, was denoted by Kalends and signified the first day of the month; the first quarter moon fell on either the fifth or seventh day of the month and was referred to as Nones; the full moon fell on either the 13th or 15th day of the month and was referred to as Ides. The ides of March—March 15—initially marked the first full moon of a new year."
Because of the significance of the day in the lunar cycle, it was marked by religious ceremonies, that is until it became the notorious day that Julius Caesar was assassinated in 44BC. The day became even more notorious thanks to Shakespeare's 1601 play Julius Caesar which gave birth to the famous warning: "Beware the Ides of March."
Interestingly, Caesar's murder is not the only terrible thing that has happened on this day. Smithsonian.com has compiled a list of ten pretty epic historic events that have occurred, including a cyclone in the Samoan Islands that destroyed six warships in 1889, Czar Nicholas II of Russia abdicating his throne in 1917, CBS cancelling the Ed Sullivan Show in 1971, and a global health alert being issued in 2003 that turned out to be SARS.
Maybe there's something to Shakespeare's warning after all...