When Julius Caesar created the Julian calendar, he made 1st January the first day of the year after the Roman God Janus. Janus was the god of doors and gates and Caesar thought it would be appropriate for January to be the doorway to a new year as it was the namesake of Janus. And because a new consuls took office that day, this also put the calendar year in line with the consular year. As the Roman armies conquered new lands, the Julian calendar was a political tool and weapon for Caesar. Some freedom in retaining certain religious and social customs was often given by the Empire to its new subjects. This calendar was used in every corner of the Empire after it was created, not just for consistency, but to remind all citizens of Roman authority and Caesar's power.
After the fall of Roman Empire, the first day of the year was moved to a more agreeable date to Christianize it as by then Christianity had spread through Europe and the celebration of the new year by Romans was seen as pagan by them. That more agreeable date for some countries was March 25 (On this day Christians commemorate the announcement to Mary that she miraculously was pregnant), while some countries used Christmas day and some countries used Easter Sunday as new year day no matter what date they fell on. Because regular non-clergy, non-royal folks didn't see a need to change the new year day, January 1 was still the first day of the year in common usage.
During the middle ages, a frustrated pope put and end to this calendrical chaos after it worked for a while. The Julian year became misaligned with the solar year because there was an error in Caesar's calendar. This difference had grown to 10 days by 1852. Pope Gregory XIII was tired of having to re-set the Spring Equinox and, with it, Easter as it kept getting moved up over the years. Gregory devised a new calendar in which he used a single leap day every four years to keep it aligned and he also restored January 1 as the first day of the year.
The Protestant and Eastern Rite countries were a little hesitant in adopting the Gregorian calendar in comparison of most Catholic countries. The Protestants complaints that they were made to worship on wrong days by the “Roman Antichrist”. Some Eastern European countries kept the Julian calendar for centuries more because the Eastern Rite churches wanted to maintain tradition. Russia only switched to Gregorian calendar after the 1917 revolution. The Eastern Orthodox Church still follows either the traditional or revised Julian calendar to set its liturgical year.