CE stands for Christian Era or Common Era. It's an alternative to AD. It's used because AD or Anno Domini means literally "In the year of our lord". Non-Christians, (Atheists and followers of Non-Christian Religions) don't always like giving the impression that they think Jesus is lord.
BCE means before the Christian Era or before the Common Era. It's an alternative to BC. Again BC means literally, Before Christ or "Before the savior". Non-Christians don't always like giving the impression that they think Jesus is the savior.