BC (B.C.) is an abbreviation used in the Julian calendar, then later the Gregorian calendar (introduced in October 1582), that means "before Christ." The letters AD (A.D.), although commonly thought to represent "After Death," actually stand for "Anno Domini," a Medieval Latin phrase that is translated as "in the year of our Lord." The original designation for this type of year also included the Latin words "Jesu Christi" or "Jesus Christ" written after the word "Lord."
Years "before Christ" are traditionally written with the year followed by the abbreviation (e.g. 100 BC). Any year at or after his believed birth can be written with the abbreviation either before or after the number (e.g. AD 100).
Assumptions
Our modern numbering system for years got its start in 525 AD by a Catholic monk who sought to compute the dates for the church's Easter festival. He laid the groundwork for the later use of BC and AD (Origin & History of the BCE / CE Dating System) which began to receive widespread acceptance during the reign of Charlemagne.
Based on this system it is natural to assume Jesus was born in 1 A.D. This, however, is not correct. Many historians and researchers have determined that the original numbering of years is off from between one to six years! Biblestudy.org's detailed timeline of Christ's birth places it in 5 BC.
The Change
B.C.E. stands for "before common era" while C.E. is short for "common era." Their popularity has grown significantly in the 21st century. Today, everything from scientific publications, school textbooks, news reporting and even Biblical commentaries have changed to using the new abbreviations.
Why has the change from BC and AD to something different and generic become more pervasive? It certainly isn't for the sake of accuracy, as the same year numbering system is still used! In September 2011, the British newspaper The Daily Mail wrote about the BBC moving to use BCE / CE for all their dates.
"The BBC has been accused of 'absurd political correctness' after dropping the terms BC and AD in case they offend non-Christians." (BBC turns its back on year of Our Lord, Daily Mail, Sept. 2011).
The article went on to quote the BBC who officially stated it was using the new terms because they were a "religiously neutral alternative" compared to the old format.
Reasons
Many have changed from using BC and AD because they feel it removes a "religious bias" toward Christianity brought by their use. The drive to be viewed as inclusive, and at least appearing to not overtly "offend" a group of people (although offending Christians seems to be OK), is also a part of the change.
The meaning of BC and AD, and what they stand for, revolves around the words "Christ" and "Lord." These titles (Strong's Concordance #G5547 and #G2962) identify Jesus as mankind's one and only Messiah. They declare that He (with the Father), as members of the Godhead, are the only ones worthy of man's undivided worship. It is therefore not surprising that many are offended when His name and authority are referenced.