This is from calare "to announce solemnly, call out," as the priests did in proclaiming the new moon that marked the calends, from PIE root *kele- (2) "to shout." In Rome, new moons were not calculated mathematically but rather observed by the priests from the Capitol; when they saw it, they would "declare" the number of days till the nones (five or seven, depending on the month). The word was taken by the early Church for its register list of saints and their feast days. Meaning "list of documents arranged chronologically" is from late 15c.
The -ar spelling in English is 17c. to differentiate it from the now-obscure calender "cloth-presser." Related: Calendarial; calendary.
A necessary process in the Roman calendar to balance the solar and lunar aspects of it. Intercalation was done after Feb. 23 or 24 (the terminalia), every two or four years. Twenty-seven days were intercalated, making a full intercalary month (which included the last four or five days of Februarius), known as mensis intercalaris (and also known, according to Plutarch, as Mercedonius). No one now knows why the intercalation was done in the middle of February rather than after its end, unless it was because the important festivals at the end of that month (Regifugium and Equirra) were closely associated with holidays in early March. After Caesar's reform (46 B.C.E.) the only intercalary day is Feb. 29 every four years.
late Old English, from Latin October (mensis), from octo "eight," from PIE root *octo(u)- "eight" (see eight). The eighth month of the old Roman calendar (pre-46 B.C.E.), which began the year in March. For -ber see December. Replaced Old English winterfylleð. In Russian history, the October Revolution (in which the Bolsheviks overthrew the Provisional Government) happened Nov. 7, 1917, but because Russia had not at that time adopted the Gregorian calendar reform, this date was reckoned there (Old Style) as Oct. 25.