BC and BCE represent a particular period in the dating system of man's history. Initially, BC, which means Before Christ, was used to describe the era before the birth of Jesus Christ. That is why it is very common to see people using something like 7 BC to refer to an era before the birth of Christ.
However, the usage of BC and AD has been disputed by many people, religious organizations, who thought it is very inappropriate to be using AD and BC notations when many scientific reports have come out to show that Jesus Christ was born in the BC era, specifically sometime between (7-4 BC).
This argument has been why such notations would be used after Jesus Christ when it has been proven that he was born in the BC era. However, to most Christians, BC and AD are still being considered as the right notations. In contrast, BCE, which means "Before the Common Era," was developed so that this era will not be based on Christian origins.