Rather than assigning an increasing number to each year, like the modern Gregorian calendar, the ancient Romans usually used an eponymous dating system where events were dated by the names of Rome's chief magistrates (typically two consuls).
Today known as the Varronian Chronology (from one of its early adopters, the famous antiquarian Marcus Terentius Varro), this chronology was made official by the early Roman Empire and has remained the standard ever since.