What is the Full Form of BCE ?

BCE - Before the Common Era

Before the Common Era is a non-religious alternative of BC (Before Christ). BCE and CE represents the same year, i.e the year 2014 BC is the same as 2014 BCE. Similar to BCE is the CE (Common Era) which is an alternative to AD (Anno Domini). 

The BC/BCE labeling system was introduced to make the dating system non-specific to a particular religion. Not all the people in the world are Christians, so it makes no sense for them to make use of a date system which is based on the lord of Christians.