Simple Definition:

BCE stands for "Before Common Era" and it is a way to denote historical dates that occurred before the birth of Jesus Christ. It is used as an alternative to the traditional "BC" (Before Christ) designation. For example, the year 300 BCE means 300 years before the birth of Jesus.

Very Simple Definition:

BCE means "Before Common Era" and it is used to talk about dates that happened before Jesus Christ was born. It is similar to saying "before Jesus was born." For example, when people talk about events that happened in 500 BCE, it means those events happened 500 years before Jesus was born.