The Gregorian year is 365 days in 3 years out of 4, then 366 in the leap year. The tropical year – the time it takes the planet to circle the sun is 365.242199 days. That difference from 365.25 is why we had a leap year back in 2000 but didn’t in 1900. It’s complicated, but the shifting dates on solstices and equinoxes provided the data for development of the Gregorian calendar.
The Roman calendar, prior to Julius’ corrections, worked with a 355 day year, with some extras thrown in every so often. It was a hard system to know what year it was. Julius wasn’t a great astronomer or mathematician, but he did want to get his supplies on time – so calendar reform was important to him. The Julian calendar consisted of 365 day years and a 366 day leap year every fourth year – essentially the same as the calendar we’ve known all our lives (despite the fact that we live under the Gregorian calendar – where a year is 365.2425 days.
His calendar was instituted in 45 BC, and was the standard until 1582. After 1627 years, that extra 0.0075 had added up to 12 days – and that would not have been a big deal if it weren’t for the solstice and equinox. Even with poor equipment and cloudy days, the error showed up (reliable clocks just weren’t around yet). Add in about sixty years of a math error calling every third year a leap year, the problem became too big to ignore.
Still, Julius Caesar’s calendar was almost the same as our own – the thing is, every time the century turns over, it’s only a leap year if the year can be divided by 400. Since 1900 wasn’t a leap year, and 2000 was, for our lifetimes, there has been no difference between the Gregorian and Julian calendars. Some of our youngest readers will live past February 28, 2100 – and experience the Gregorian calendar.
As for why February gets the extra day? Those old Romans started the year with March, not January.