BCE stands for "Before the Common Era" and it is basically equivalent to "BC", except that it doesn't have the Christian religious connotations of BC. That makes the usage preferable for some scholars.
Unfortunately, in our contentious world, using BCE also sometimes offends people, some of whom have suggested that we use plus signs and minus signs to indicate the years before the Julian calendar start date of 1 (there's no 0 in Julian).
Similarly, the abbreviation C.E. means "the Common Era." And it starts with the Julian calendar 1.
Proper Usage: 10 BCE, 133 CE
Other Common Calendar Designations
Taylor, Timothy 2008 Pehistory vs. Archaeology: Terms of Engagement. Journal of World Prehistory 2:11–18.