Our everyday life depends upon the accurate and standardized form of time-keeping that we are used to and often take for granted, we usually never give a second thought to these things. There are a lot of calendars being used by people around the world but the one we all know and use is known as the "Gregorian Calendar", it was named after Pope Gregory XIII.
Before the Gregorian calendar was standardized, people around the world used their own calendars (some being more accurate than others), like most of the Western countries used the Julian calendar, which was named after Julius Caesar, Chinese people used their own lunisolar calendar, In India people used a calendar called Panchanga and it is still used to calculate Hindu festivals.
The reason the Gregorian calendar is the international standard used almost everywhere in the world to mark the passing of time might be a little more complicated than you might have thought. It takes 365 days, 5 hours, 48 minutes, and 46 seconds for the Earth to make a full revolution around the sun; Things would be a lot easier if it was even 365 days.
Most of the Western world used the Julian calendar, The Julian calendar had 365 days every year with an extra day every four years. This was pretty accurate, but it made a year on average 11 minutes and 14 seconds too long. But nobody took notice and this little glitch wouldn't be dealt with until 1582. That's the year that the Gregorian calendar started finally being used. That 11-minute glitch in the Julian calendar created a problem with Easter. It was supposed to be celebrated on the Sunday after the first full moon after the spring equinox, or March 21st. But as it slipped later and later each year, Pope Gregory got concerned, so he commissioned scientists and astronomers to get this right. After calculating, they realized that t**he traditional calendar had fallen 10 full days behind over the years.**
To rectify this, steps needed to be taken.
In 1582, October 5 Never Happened. On Oct. 5, 1582, most of Europe replaced the Julian calendar with the Gregorian calendar; the process of switching required that the 10 days after Oct. 4 should be skipped. The Gregorian calendar is more accurate than the Julian because it still had a leap year every four years, except for years that are divisible by 100, and unless that year is divisible by 400 so 2000 was a leap year, but 2100 will not be (it's messed up). Of course, nothing's perfect, and the Gregorian calendar is no exception: in 4909, is will be a full day ahead, but hopefully by then, we humans will be capable enough to figure things out.
Also, another fun fact, the reason it's 2015 and not 2768 is that in the year 525, Christian Monk Dionysius Exiguus determined that Jesus was born in the Roman year 753, and reset the year from there (although it's generally accepted that he was off by about 5-6 years). We can also blame Exiguus for the denominations BC (before Christ) and AD (Anno Domini, Latin for "The Year of Our Lord").
Academic and scientific communities have been increasingly using the more neutral, less Christianity-centric BCE and CE for "Before Common Era" and "Common Era". Of course, there are tonnes of other calendars that people use, and even some really intriguing calendars that were developed like the Tranquility calendar, which starts on the day we landed on the Moon, and has 13 28-day months, all named after scientists.
In case you want to read/watch some more on this topic.