What does BCE mean when talking about a year thousands of years ago? ?

Just do Like I do BC is before Christ and i dont care if it offends Atheists

It is a fancy way of dissing religion, which is always awesome. Before Common Era

Before the Common Era.

Before Common Era.  Science requires precision, and the term BC is both a religious term and so not favored, and somewhat uncertain in actual fact (no one really knows the year that Jesus was born; there have been arguments about it).  So, what they did was say "we call this year, x numbers of years before present on the day we declare this, as the marker year, and we will call it "common era" to indicate that is the common usage at the time we write this; year 1 on the current commonly used system for counting years is the start of the Common Era.

There is no year 0, just to be clear.  There is a zero point, which is when 1 BCE become 1 CE.  the year count goes directly from 1 BCE to 1 CE.  No 0.

Science does not abide uncertainty or ambiguity very well.  Science requires everyone to mean exactly the same thing when they say something.  It can be a pain in the butt sometimes, but it has to be that way.

BCE means Before the Common Era; specifically, prior to year zero. Starting with year zero, the current time, often referred to as AD, becomes CE or Common Era, meaning now.

non-Christian people are saying Before Christian Era (instead of Before Christ)

Common era. Since many peoples do not peg time to Christ 

CE and BCE have been used in some areas since about the 1880s.

They mean "Common Era" and "Before the Common Era."

Their academic use became widespread in the mid-1990s.

BCE (Before Common Era) is considered more politically correct.  Ridiculous.