One of my calendars.

The Romans did not number days of a month sequentially from the first through the last day. Instead, they counted back from three fixed points of the month:

• The Nones (5th or 7th, depending on the length of the month), 

• The Ides (13th or 15th), 

• The Kalends (1st) of the following month. 

The Ides occurred near the midpoint, on the 13th for most months, but on the 15th for March, May, July, and October. The Ides were supposed to be determined by the full moon, reflecting the lunar origin of the Roman calendar. On the earliest calendar, the Ides of March would have been the first full moon of the new year. [skullion]

Religious observances

The Ides of each month was sacred to Jupiter, the supreme deity of the Romans. The Flamen Dialis, Jupiter's high priest, led the "Ides sheep" (ovis Idulius) in procession along the Via Sacra to the arx, where it was sacrificed.^[3]

In addition to the monthly sacrifice, the Ides of March was also the occasion of the Feast of Anna Perenna, a goddess of the year (Latin annus) whose festival originally concluded the ceremonies of the new year. The day was enthusiastically celebrated among the common people with picnics, drinking, and revelry.

One source from late antiquity also places the Mamuralia on the Ides of March.
This observance, which has aspects of scapegoat or ancient Greek pharmakos ritual, involved beating an old man dressed in animal skins and perhaps driving him from the city. The ritual may have been a new year festival representing the expulsion of the old year.

In the later Imperial period, the Ides began a "holy week" of festivals
for Cybele and Attis. The Ides was the day of Canna intrat ("The Reed enters"), when Attis was born and exposed as an infant among the reeds of a Phrygian river.

He was discovered—depending on the version of the myth—by either shepherds or the goddess Cybele, who was also known as the Magna Mater, "Great Mother".

A week later, on 22 March, the day of Arbor intrat ("The Tree enters") commemorated the death of Attis under a pine tree. A college of priests called "tree bearers" (dendrophoroi) cut down a tree, suspended from it an image of Attis, and carried it to the temple of the Magna Mater with lamentations.

The day was formalized as part of the official Roman calendar under Claudius. A three-day period of mourning followed, culminating with the rebirth of Attis on 25 March, the date of the vernal equinox on the Julian calendar

Sources
Wikipedia
H.H. Scullard,  Festivals and Ceremonies of the Roman Republic (Cornell University Press, 1981), pp. 42–43

Images @ Eminpee Fotography