1 CE is considered the first year of the modern calendar. It is the same year as 1 AD, the time of the anno domini system. The year before 1 CE is 1 BCE, as with the anno domini system (where 1 CE is preceded by 1 BC). The title "CE", for Common Era or Christian Era was proposed as a secular substitute for anno domini, which some people believe implies acceptance of the Christian belief of Jesus as divine.
The anno domini system was created by Dionysius Exiguus in the year 525, believing that the date was 525 years after the birth of Jesus. This system was adopted by the early Christian church, primarily at the urging of Bede, and spread with throughout Europe and to the rest of the world. This became an important part of the Gregorian calendar, which was defined and controlled by the Roman Catholic Church.
However, even to Bede, it was evident that an error had been made in the original calculations. The birth of Jesus is now believed to have happened several years before 1 CE; the current belief is that Jesus was born four years before the original calculations held him to be born, at 4 BCE.