What does BCE mean?
The word BCE means, "Before Common Era". It is the term more commonly used now among historians, rather than BC which is the abbrevation for "Before (the birth of) (Jesus) Christ". I think I remember reading that the date of the birth of Jesus Christ was mistaken, and is actually AD 6 (i.e. 6 years later than the date people thought). To avoid confusion of dates, the wrong BC (before christ) was made BCE. And AD Anno Domini) was made to CE (Common Era).
Using BCE instead of BC does not make the actual date any more precise.
It is also mainly used because of its political correctness. Obviously Christianity isn't the only view people have so Common Era (the past 2011 years) and Before Common Era (Everything before that) would be more polite. Some Christians do not like this choice because it isn't acknowledging their religion, however, the C in CE and BCE can be said as Current, Common, or Christian.