The early Roman calendar was defined by the phases of the moon. The three most important days in each month were the kalends (from which we get the word 'calendar'), the ides, and the nones. These three days marked, respectively, the dates of the new moon, the full moon, and the half moon.
In the early days, the Kalends, the ides and the nones would be announced publicly according to astronomical observations. But as the calendar became more sophisticated, they became fixed within each month. The kalends was always the first day of the month; the ides would be around the middle of the month, and the nones would be eight days before the ides. (The word 'nones' is derived from novem, the Latin word for 'nine'; the nones is the ninth day if you consider the ides as the first day and count back.) So in the longer months (those with 31 days), the ides would generally be the 15th and the nones would be the 7th; in the shorter months, the dates would be the 13th and the 5th respectively.
March having 31 days, the Ides of March is (as every quizzer should know) the 15th. Julius Caesar was assassinated on 15 March, 44 BC.
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