The year numbering now used almost everywhere was produced as a by product of a calendar problem. Easter falls on a Sunday determined by the moon, and computing it years in advance required tables. In 525 the monk Dionysius Exiguus, working in Rome, extended an existing set of Easter tables and chose to number the years from the incarnation rather than from the reign of the emperor Diocletian, whose era the older tables used and who was remembered as a persecutor.
The Oxford Companion to the Year sets out how the scheme spread, slowly, through the work of Bede and others, and how long it took to displace the many local systems of reckoning by regnal year, by indiction and by city foundation. Two consequences follow that are frequently missed. The system has no year zero, so the year before 1 is 1 before the era, which is why century boundaries fall where they do. And the calculation itself is generally reckoned to be several years out from the dates the gospel accounts imply, so the era named for the birth of Jesus most likely does not begin at it. Neither point was a mistake anyone could have avoided with the information available in 525, and neither has ever been corrected, because renumbering every date in every document ever written is not a serious proposal. The era is therefore a Christian calculation, made for a liturgical purpose, that the whole world now uses for reasons that have nothing to do with either.