What day does the first of the year fall on? It wasn't always January 1st.
The ancient Babylonians, for example, celebrated the beginning of a new year on what is now March 23, although they didn't have a written calendar - no mean feat considering that this was long before the ubiquitous datebooks and wall calendars we can't live without.
Time passed, and with it came the development of the ancient Roman calendar, which was based on a lunar system. Better, but still not very accurate.
Then, in 46 B.C., Julius Caesar introduced a new, solar-based calendar (the Julian calendar). This was a vast improvement on the Roman calendar, which had become wildly inaccurate over the years. The Julian calendar decreed that the new year would occur on January 1st, and within the Roman world, this became the consistently observed start of the new year.