BCE stands for Before Common Era. It is used the same way as the traditional abbreviation BC (Before Christ) and also has the same meaning "previous to year 1 CE (Common Era). BCE is a recent term that is used in place of BC, e.g., 200 BC, and 200 BCE has the same meaning.
Today, most of the countries and educational institutes have officially replaced the traditional abbreviations AD/BC with CE/BCE. For example, Wales and England introduced the CE/BCE system into their official school curriculum in 2002. Australia followed it in 2011. Also, in the United States, most of the history tests and textbooks use CE/BCE.
A year written without letters (CE or BCE) is considered a Common Era, starting from year 1. CE or BCE should be used if there are chances of misunderstanding, e.g., in texts where years both before and after year 1 are mentioned. For example, the ancient city was founded around 200-300 BCE but was destroyed in 80 CE due to volcanic eruptions, floods, and earthquake.