Common Era is a method of date notation that equates to the universally understood AD or anno domini notation. It was introduced by a group of American historians concerned that, if they did not change date jargon, there was a danger that some non-historians, or even worse non-American historians, might understand what the hell they were going on about.
For instance, most English schoolboys learn that Julius Caesar invaded Britain in 55 BC, and then again one year later in 54 BC, as outlined in his book The Gallic Wars, which describes his invasion of France. Some historians believe this is too straightforward and prefer to say he invaded Britain in 55 BCE - thereby, by the devilish insertion of the letter "E" making everyone else think - what the fuck does he mean?
Common Era designation is particularly popular amongst Jewish historians, worried that unless they deliberately choose language that non-Jews have no chance of comprehending, that Gentiles may actually understand what Judaism is about and stop persecuting them. Much better to promote division and differences, letting them write about all the religious hatred and thereby sell more books to other Jews complaining about it all. Of course, their attempts at confusion go well beyond this, and include deliberately including Hebrew, and making sure that no-one can go beyond the first paragraph of their writings unless they have an accumulated knowledge of all things Jewish.
As with all forms of political correctness, adherents of the neologism maintain that those who do not adopt it are being deliberately offensive, are bigoted, and support worldwide religious intolerance. This is especially true of someone who has never heard of there neologism, but is an approach promoted to ensure that the PCers offend as many people as possible. The PC lobby can already claim some success with common era notation - with their successes including pissing off the official opposition in the New South Wales parliament, many angry letters to newspapers, and holding the Royal Ontario Museum open to public ridicule.