The designations BCE and CE are simply a different way to write the traditional BC and AD. The basis of our modern calendar was developed by Christian monks in the Middle Ages who decided to begin numbering years with the birth of Christ, and designate that year "0" (most historians agree that they miscalculated the year and the actual date of the birth of Christ was between 6 BC and 4 BC by the present calendar). Years following year 0 were designated AD, for the Latin anno Domini, "in the year of the Lord. Years counting backward before year 0 came to be designated BC, before Christ. These designations were eventually adopted on an almost global scale. A few religious traditions objected to the religious overtones of the calendar and so, for example, both Islam and Judaism use a different numbering of years for religious calendars.
In modern times, in an era of political correctness and multicultural sensitivity, some tried to find more religiously neutral ways of referring to calendar years. This was particularly the case in the academic world that frequently had to use both BC and AD dates in interaction with people that represented other world religions. So, the designations BCE, Before the Common Era, and CE, the Common Era, were adopted in order to retain a long established way of counting years, and yet remove some of the Christian religious confession inherent in the traditional designations. Most people still use the older designations as a matter of accepted practice and convenience, but especially in international academic writing the newer abbreviations are common.
-Dennis Bratcher