The meaning of AD is  Anno Domini or Year of our Lord referring to the year of Christ’s birth.   The meaning of BC is  Before Christ.  CE is a recent term.  It refers to Common Era and is used in place of A.D. the dates are the same ie 2009 AD is 2009 CE.  BCE means Before Common Era.  For example 400 BC is 400 BCE.  

Many different calendars have been used since man began tracking time.  Most start with some epoch event or person.  The use of BC and AD for numbering calendar years was invented by Dionysius Exiguus in 525 AD.  His purpose was to determine the correct date for Easter under the direction of Pope St. John I. 

Prior to this time, one method for determining Easter was based on a 532 year calendar cycle stemming from the Alexandrian era.  Other methods were also used which led to the confusion.  Dionysius was asked to determine a method for calculating Easter that would then be used by the entire church.

Dionysius did not want to perpetuate the name of Alexander, the Great Persecutor.  He decided to start his 532 year cycle from the year associated with the foundation of Rome.  At that time Christ’s birth was supposed to have occurred immediately preceding the year of the founding of Rome.  Today, based on historical evidence relating to Herod and astronomical evidence relating to eclipses and star novas, most historians believe Christ was actually born a few years earlier.

Dionysius named the years relating to his cycle, BC meaning Before Christ which starts with year 1 and AD meaning Anno Domini, the year of Our Lord referring to the year of Christ’s birth.  This is also a year 1.  There is no year 0.  (That’s the reason purists insists the 21st century actually began January 1, 2001.   For example the first year began in 1 AD and ended the beginning of  2 AD so the first year of the 21st century begins in 2001 AD and ends with the beginning of 2002 AD)

It took about 400 years for the dating system devised by Dionysius to reach common usage.    In combination with the Julian Calendar system which determines the beginning of months and years this continued until 1582 AD.   The number of each year is based on the Dionysius numbering system. 

The need for the introduction of the Gregorian Calendar came about because a year is not exactly 365 days long.  It is actually 365 and a quarter days long.  Every 4 years, March 1st moved behind a day until after centuries instead of being early spring March 1st was now the beginning of winter.  Something had to be done.

The Gregorian Calendar was introduced in the Catholic parts of Europe in 1582 A.D.  by Pope Gregory XIII (then the religious leader of the Roman Catholic faith) as an improvement upon the Julian Calendar to keep the average length of the calendar year better in line with the seasons. 

Now here's a rule that will drive you crazy.  The rules, months, and days of the Gregorian calendar are the same as those of the Julian Calendar, except for the leap year rules. In the Gregorian calendar, a year is a leap year if the year number is evenly divisible by 4, but not if the year number is evenly divisible by 100.  The 100 year rule is not applied if the year number is evenly divisible by 400. For example, 1600 and 2000 are leap years, but 1700, 1800, and 1900 are not. 

"The legal code of the United States does not specify an official national calendar. Use of the Gregorian calendar in the United States is a result of an Act of Parliament of the United Kingdom in 1751, which specified use of the Gregorian calendar in England and its colonies. However, its adoption in the United Kingdom and other countries was fraught with confusion, controversy, and even violence. It also had a deeper cultural impact through the disruption of traditional festivals and calendrical practices." (Seidelmann, P. Kenneth, Explanatory Supplement, United States Naval Observatory. Nautical Almanac, pg. 578)

The widespread use of the Gregorian calendar and the use of BC and AD throughout the world came about thanks to the colonization practices of Europe and economic pressures of a world-wide economy led by Europe and the United States.  This is gradually changing as more and more academic writers prefer the use of CE rather than AD.