Februarius was, with January, one of the two months Roman tradition says King Numa added to close the winter gap of the old ten month year, and it long stood last in the Roman year rather than second. Its name comes from the februa, the strips, branches and other instruments of purification used in the month's rites; Ovid opens the second book of the Fasti with exactly this explanation, deriving the month from the act of cleansing that prepared the community for the year that began in March. The Lupercalia of the fifteenth of February, when the luperci ran their circuit striking bystanders with goatskin thongs, was the most famous of these purifications, and the Parentalia in the middle of the month turned the same instinct toward the family dead, honoured at their tombs with offerings.
February's shortness and its leap day are both Roman inheritances. As the final month of the old year it absorbed the arithmetic left over by the others, and the Roman intercalary month, when the priests inserted one, was spliced into late February; Julius Caesar's reform of 46 BCE replaced that clumsy device with a single day added every fourth year in the same place. The Gregorian reform of 1582, promulgated by Pope Gregory XIII, kept February's leap day but skips it in three century years out of four, the adjustment that still holds the calendar to the sun.
Only when the first of January became the civil new year did February become the second month rather than the last, a reordering already settled by the late Roman Republic.
Sources FastiOvid with The Oxford Companion to the Year: An Exploration of Calendar Customs and Time-ReckoningBonnie Blackburn and Leofranc Holford-Strevens