When it was BC and AD as a kid I was taught it had something to do with Jesus, but obviously having grown up and the terminology changing I was hoping I could learn the real reason.
It's not really accurate to say, as /u/Akibiades415 implied, that AD is "widely used" by 800. There are certainly examples of its use by then, probably most famously by Bede. In the early and high Middle Ages, probably AD dating shows up most often in chronicles--that is, texts concerned with placing the events of a king's reign or a monastery's existence within the wider scope of salvation history. After 1000 and especially 1100, as we start to have more and more charters, letters, miscellaneous legal documents, the ongoing plurality of systems of dating is readily apparent. Sometimes even the same document will offer two forms of date--how many years into the local lord's reign; how many years into the pope's reign. Of course, when we look at merchants' documents from Jewish Europeans, they use regnal dating or the Jewish calendar, too!
Michael Clanchy talks a little about the gradual triumph of Anno Domini in From Memory to Written Record. Throughout the book, he argues that between 1066 and 1300, English people (Europeans) began to understand written texts in a new way. Rather than being symbols, they became sources of information to be consulted. So a charter transferring land ownership dated the 12th year of Lord John's reign would not have the same resonance to people involved in land disputes 115 years later who had no memory of "Lord John." In 1070, Clanchy argues, the new Norman conquerors had no concept of trusting or consulting written texts for information. By 1300, they did. And by the late Middle Ages, indeed, AD is the standard for dating.
And all of this is only to discuss Latin Europe. I'm not familiar with the time frame in which the Eastern churches (various Eastern Orthodox and Oriental Orthodox churches) adopted AD, much less non-colonized non-European countries.
"Common era" has been in use since the 17th Century, it isn't new. It was mostly used by Jewish writers who didn't want to call Jesus "Lord" or "Messiah." For Jews it is still "BC."
Another issue with the BC/AD system is that it's inaccurate. If Jesus was born during the reign of Herod the Great, then he could not have been been later than 4 BCE because Herod died in 4 BCE.
As a matter of academic accuracy and religious objectivity BCE/CE has become preferred in academic journals, but it's still largely a matter of personal preference.