Intercalary months, however, were not necessarily regular. Historians are still unclear as to how the early Romans kept track of their years, mostly because the Romans themselves may not have been entirely sure. It appears that the early Roman calendar consisted of ten months plus an ill-defined winter period, the varying length of which caused the calendar to become unpegged from the solar year. Eventually, this uncertain stretch of time was replaced by the new months of January and February, but the situation remained complicated. They employed a 23-day intercalary month known as Mercedonius to account for the difference between their year and the solar year, inserting it not between months but within the month of February for reasons that may have been related to lunar cycles.

To make matters even more confusing, the decision of when to hold Mercedonius often fell to the consuls, who used their ability to shorten or extend the year to their own political ends. As a result, by the time of Julius Caesar, the Roman year and the solar year were thoroughly out of sync.

The Mercedonius-when-we-feel-like-it system apparently irked Caesar, the general-turned-consul-turned-dictator of Rome who drastically altered the course of European history. In addition to conquering Gaul and transforming Rome from a republic into an empire, Caesar re-ordered the Roman calendar, giving us the blueprint off of which much of the world still operates to this day.

During his time in Egypt, Caesar became convinced of the superiority of the Egyptian solar calendar, which featured 365 days and an occasional intercalary month which was inserted when astronomers observed the correct conditions in the stars. Caesar and the philosopher Sosigenes of Alexandria made one important modification: instead of relying on the stars, they would simply add a day to every fourth year. In keeping with the Roman tradition of messing with the length of February, that day would fall in the second month of the year—thus Leap Day was born. Caesar added two extra-long months to the year 46 BCE to make up for missed intercalations, and the Julian Calendar took effect on January 1st, 45 BCE.

https://www.history.com/news/why-do-we-have-leap-year