Short answers, pulled from the story.
The Julian calendar is a solar calendar of 365 days, with an additional leap day every fourth year without exception. It follows a simple cycle of three normal years and one leap year, giving an average year of 365.25 days.
The Julian calendar was proposed in 46 BC by Julius Caesar, who gave it his name, as a reform of the earlier Roman calendar. It took effect on the 1st of January 45 BC by his edict.
The Julian calendar was replaced because its average year of 365.25 days was longer than the tropical year, causing it to gain one day every 128 years. By 1582, the 21st of March had drifted ten days from the March equinox, so Pope Gregory XIII promulgated a revised calendar.
The last year of confusion was 46 BC, which ran for 445 days, the longest year in Roman history. Caesar lengthened it to compensate for intercalations missed during his pontificate, adding 67 days through two extraordinary intercalary months between November and December.
The Julian calendar is still used as a religious calendar in parts of the Eastern Orthodox Church and parts of Oriental Orthodoxy, and in the Berber calendar of the Maghreb. Orthodox churches including those of Jerusalem, Russia, and Serbia celebrate the Nativity on the 25th of December Julian, and Foula in Shetland keeps its festivities by the Julian calendar.
Between 1901 and 2099, the Gregorian date equals the Julian date plus 13 days. For example, the 1st of January Julian falls on the 14th of January Gregorian.
For thirty-six years, the pontifices added a leap day every three years instead of every four, inserting twelve intercalary days instead of the nine actually due. Augustus corrected the error by ordering twelve years to pass without any leap day.