Rome’s second king, Numa Pompilius, felt kind of bad about those unnamed extra winter days, so he came up with two new months: Januarius and Februarius. King Numa tacked his new months onto the beginning of the year, which bumped all the other months back. That wasn’t such a big deal for the first four months, which were named for gods (Mars, Aphrodite, Maia, Juno)—but it’s darned awkward for the other months, which were named for their numbered positions in the year. ‘September’ means ‘seventh month’ but now it’s the ninth. October means eighth, but it’s the tenth. November means ninth, but it’s the eleventh. December means tenth, but it’s the twelfth.
The calendar year still kept coming up 10 days too short, so every 2-3 years a leap month—Intercalaris—was added.
In 45 bc, Julius Caesar reformed the Roman calendar by uncoupling it from the Moon—no more figuring out lunar cycles. He must have decided that having a set number of days in a year—365—meant fewer headaches when running something as big as the Roman Empire. Julius ditched the leap month. But because a year is actually 365 days and 6 hours, he added an extra day (February 29) every fourth year—the Leap Year.
What about Quintilis and Sextilis? Quintilis (means ‘fifth month,’ now it’s the seventh) was renamed July for Julius Caesar and Sextilis (means ‘sixth month,’ now it’s the eighth) was renamed August for Caesar Augustus (Julius’ nephew and Rome’s first emperor).
This was the Julian Calendar. It’s more or less the same one we use today.