Origin

From Shakespeare's Julius Caesar, 1601. 'Beware the Ides of March' is the soothsayer's message to Julius Caesar, warning of his death.

The Ides of March didn't signify anything special in itself - this was just the usual way of saying "March 15th." Each month has an Ides (usually the 15th) and this date wasn't significant in being associated with death.

Months of the Roman calendar were arranged around three named days and these were reference points from which the other (unnamed) days were calculated:

Kalends (1st day of the month).
Nones (the 7th day in March, May, July, and October; the 5th in the other months).
Ides (the 15th day in March, May, July, and October; the 13th in the other months).