The system was devised when Rome was a Republic, and the consuls were elected in pairs and changed annually to avoid either becoming too powerful.
The 365-and-change-day calendar we use is the result of scientific sweat, an attempt to bring us to a Verifiable Truth regarding how long it takes the Earth to complete one rotation around the sun. Starting a calendar 4.54 billion years ago doesn't make much intuitive sense.
As a result, his determination of the birth year of Christ was apparently off by about 4 years, but the error was not realized until centuries after the system had come into general use, leading to the strange circumstance that Christ was actually born in approximately 4 BC.
The designations BC and AD deserve a brief explanation at this point.
Under our calendar, he was probably born in the spring of 6 BC, rendering the BC and AD terms ludicrous.
Our calendar is now so thoroughly established, however, that it is easier to rename than to renumber.