The year is the time taken by the Earth for one full orbit around the Sun. At the end of that time, the Earth is back to the same point in its orbit, and the Sun is therefore back to the same apparent position in the sky.
It takes the Earth 365.2422 days to complete its circuit (average solar days), and any calendar whose year differs from this number will gradually wander through the seasons. The ancient Roman calendar had 355 days but added a month every 2 or 4 years: it wasn't good enough, and by the time Julius Caesar became ruler of Rome, it had slipped by three months.
In 46 BC Caesar introduced a new calendar, named after him: the Julian calendar. It is similar to the one used today: the same 12 months, and an added day at the end of February every 4th year (“leap year"), on years whose number is divisible by 4. Two years afterwards the 5th month of the Roman year was renamed July, in honor of Julius. The name of his successor, Augustus Caesar, was later attached to the month following July.
The Julian calendar thus assumes a year of 365.25 days, leaving unaccounted a difference of 0.0078 days or about 1/128 of a day. Thus the calendar still slips, but at a very slow rate, about one day in 128 years. By 1582 that slippage was approaching two weeks and Pope Gregory the 13th therefore decreed a modified calendar, named after him: the Gregorian calendar. Henceforth years ending in two zeros, such as 1700, 1800, 1900--would not be leap years, except when the number of centuries was divisible by 4, such as 2000. This took away 3 “leap days" every 400 years, i. e. one day per 133 1/3 years --- close enough to the required correction of one day per 128 years.
But it was not enough to modify the calendar: a one-time jump of dates was also needed, to get rid of the accumulated difference. In Italy this was done soon after the pope's edict, and “Tibaldo and the Hole in the Calendar" by Abner Shimony spins the story of a boy whose birthday was on a day skipped by that jump. Another birthday affected was that of George Washington, born February 11, 1732: when the British empire in September 1752 implemented the Gregorian calendar, the 11th of February “old style" became the 22nd of February “new style," and nowadays that is when Washington's birthday is usually celebrated.
In Russia the change came only after the revolution, which is why the Soviet government used to celebrate the anniversary of the “October Revolution" on November 7th. The Russian orthodox church continues to use the Julian calendar and celebrates Christmas and Easter about 2 weeks later than most of the Christian world.