The calendar you're used to hasn't been around forever. For example, people in 5 BCE weren't standing around wondering who this "Christ" bloke was who they were all counting down towards. Calendars have changed for political reasons, as well as to better reflect our understanding of the year.
In 1582, Pope Gregory XIII introduced the Gregorian calendar. Prior to this, most of the Roman world and Europe had used the Julian calendar, introduced by Julius Caesar in 45 BCE.
Though the Julian calendar had functioned perfectly well as calendars go, there was a problem calculating the date of Easter, which the Council of Nicaea, in 325 CE, had decided should fall on the first Sunday following the first full moon after the vernal equinox. A few centuries later, it was noticed that the vernal equinox date set by the council – March 21 – had drifted away from the actual vernal equinox.
In order to try and link the calendar up to the solar year (the time it takes for Earth to revolve around the Sun), the Julian calendar had a leap year every four years, in which an extra day was added. The problem was that since the actual solar year is 365.24219 days, the Julian calendar quickly (and by quickly, I mean incredibly slowly) gains a day every 314 years.
To account for the movement of the equinox and solstice, when the Gregorian calendar was introduced, it was decided that the world should simply skip days. October was chosen by the church to avoid events in the Christian calendar, and after the Feast of St. Francis of Assisi on October 4, the switch to the Gregorian calendar took place, shooting everybody forward to October 15 instantly.
Pope Gregory should have shifted the date by 13 days to make up for the drift, yet after calculations by mathematicians and scientists, he only shifted it by 10.
Though the Catholic church adopted the calendar in 1582, it was an early adopter, leading to big discrepancies between the two calendars. Later adopters of the Gregorian – the UK, US, and Canada switched in 1752 – had to skip more days, with Turkey losing 13 days across 1926 and 1927.