The only important historical events that may have taken place during 1 AD are completely coincidental to the fact that our calendar era places its epoch at that year.

Most modern historians ascribe a historical Jesus Christ's birth year to between 6 BC and 4 BC, some outliers as late as 6 AD. But there is no evidence to suggest it occurred in exactly 1 AD (or the preceding year, 1 BC).

One single Christian monk who lived in the 6th century in what is now Romania/Bulgaria is the sole reason behind the fact that 1 AD was chosen as the purported year of Christ's birth, resulting in 2019 being the current year. His name was Dionysius Exiguus (commonly referred to as "Dennis the Short").

While writing some calculations about future dates for Easter in what was then referred to as the "Year of the Consulship of Probus Junior", he stated that the current year he was living in was "525 years since the Incarnation of our Lord Jesus Christ", which we now refer to as the year 525 AD. His intention was never to create a calendar era, just to make calculations for the date of Easter. No one is sure how he arrived at exactly 525 years, but for an obscure monk living in the 6th century he came pretty close to what historians now think is the correct time range. His era eventually "went viral" and became adopted as the official epoch of the Roman Catholic Church, and the rest is history.